Direct Detection of the 229Th Nuclear Clock Transition

From left to right: Peter G. Thirolf, Lars v.d. Wense, Benedict Seiferle.

Authors: Lars von der Wense¹, Benedict Seiferle¹, Mustapha Laatiaoui^2,3, Jürgen B. Neumayr¹, Hans-Jörg Maier¹, Hans-Friedrich Wirth¹, Christoph Mokry^3,4, Jörg Runke^2,4, Klaus Eberhardt^3,4, Christoph E. Düllmann^2,3,4, Norbert G. Trautmann⁴, Peter G. Thirolf¹

Affiliations:
¹Ludwig-Maximilians-Universität München, 85748 Garching, Germany.
²GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany.
³Helmholtz Institut Mainz, 55099 Mainz, Germany.
⁴Johannes Gutenberg Universität, 55099 Mainz, Germany.

The measurement of time has always been an important tool in science and society [1]. Today’s most precise time measurements are performed with optical atomic clocks, which achieve a precision of about 10^-18, corresponding to 1 second uncertainty in more than 15 billion years, a time span which is longer than the age of the universe [2]. By comparing two of such clocks, which are shifted in height by just a few centimetres, also the time dilation due to general relativistic effects becomes measurable [3].

Despite such stunning precision, these clocks could be outperformed by a different type of clock, the so called “nuclear clock” [4]. The nuclear clock makes use of a nuclear transition instead of an atomic shell transition as so far applied. The expected factor of improvement in precision of such a new type of clock has been estimated to be up to 100, in this way pushing the ability of time measurement to the next level [5]. The reason for the expected improvement is the size of the nucleus, which is orders of magnitude smaller than the size of the atom, thus leading to significantly improved resilience against external influences.

Many potential applications for a nuclear clock are currently under discussion. These include practical applications such as improved satellite-based navigational systems, data transfer, gravity detectors [6] as well as fundamental physical applications like gravitational wave detection [7] and testing for potential changes in fundamental constants [8].

Using existing technology, there is only one nuclear state known, which could serve for a nuclear clock. This is the first excited nuclear isomeric state of ²²⁹Th. Among all known (more than 175,000) nuclear excitations, this isomeric state exhibits a unique standing due to its extremely low excitation energy of only a few electronvolts [9]. The energy is that low, that it would allow for a direct laser excitation of the nuclear transition, which is the prerequisite for the development of a nuclear clock.

The existence of this isomeric state was shown in 1976, based on indirect measurements [10]. However, despite significant efforts, the direct detection of the isomeric decay could not be achieved within the past 40 years [11]. In the recently presented work [12], our group was able to solve this long-standing problem, leading to the first direct detection of the ²²⁹Th nuclear clock transition. This direct detection is important, as it paves the way for the determination of all decay parameters relevant for optical excitation of the isomeric state. It is thus a breakthrough step towards the development of a nuclear clock.

Figure 1: (click on the image to view with higher resolution) Experimental setup used for the production of a purified ²²⁹Th ion beam and the direct detection of the isomeric state. For details we refer the reader to the text and to Ref. [12].

The detection was achieved by producing a low energy, pure ²²⁹Th ion beam, with a fractional content of ²²⁹Th in the isomeric state. The isomer was produced by making use of a 2% decay branch of the alpha-decay of ²³³U into the isomeric state. The setup used for ion beam production is shown in Fig. 1 and will be described in the following section. The ions were collected with low kinetic energy onto the surface of a micro-channel-plate (MCP) detector, triggering the isomer’s decay and leading to its detection at the same time. The obtained signal is shown in Fig. 2. A high signal-to-background ratio could be achieved owing to the concept of spatial separation of the ²³³U source and the point of isomer detection. Many comparative investigations were performed in order to unambiguously show that the detected signal originates from the ²²⁹Th isomeric decay [12].

Figure 2: ²²⁹Th isomeric decay signal as observed during 2000 second integration time on the MCP detector allowing for spatially resolved signal read out.

For the production of a low-energy ²²⁹Th ion beam, a ²³³U source was used, which was placed inside of a buffer-gas stopping cell, filled with 40 mbar of ultra-pure helium. ²²⁹Th isotopes, as produced in the alpha-decay of ²³³U, are leaving this source due to their kinetic recoil energy of 84 kiloelectronvolts. These recoil isotopes were stopped in the helium buffer-gas, thereby staying charged due to the large ionization potential of helium. The low-energy ²²⁹Th ions, produced in this way, were guided through the helium background towards the exit of the stopping cell by electric fields, provided by a radio-frequency funnel system. The exit of the stopping cell consists of a Laval-nozzle system, leading to the formation of a supersonic gas jet. This gas jet injects the ions into a radio-frequency quadrupole (RFQ) ion-guide, leading to the formation of an ion beam. This ion beam is further purified with the help of a quadrupole mass-separator (QMS). In this way, a low-energy, pure ²²⁹Th ion beam was produced, possessing a fractional isomeric content of about 2%.

The next envisaged steps towards the development of a nuclear clock will be performed within the framework of the EU-funded Horizon 2020 collaboration named “NuClock” (www.nuclock.eu). Experiments will be carried out that aim for a precise determination of the isomer’s energy and half-life as being the basis for the first direct laser excitation of a nuclear transition.

References:
[1] David Landes, "Revolution in Time: Clocks and the Making of the Modern World" (Harvard University Press, Cambridge, 2000).
[2] T.L. Nicholson, S.L. Campbell, R.B. Hutson, G.E. Marti, B.J. Bloom, R.L. McNally, W. Zhang, M.D. Barrett, M.S. Safronova, G.F. Strouse, W.L. Tew, J. Ye, "Systematic evaluation of an atomic clock at 2 X 10^-18 total uncertainty", Nature Communications, 6, 6896 (2015). Abstract.
[3] Andrew D. Ludlow, Martin M. Boyd, Jun Ye, E. Peik, P. O. Schmidt, "Optical atomic clocks", Review Modern Physics, 87, 637-701 (2015). Abstract.
[4] E. Peik, Chr. Tamm, "Nuclear laser spectroscopy of the 3.5 eV transition in ²²⁹Th", Europhysics Letters, 61, 181-186 (2003). Abstract.
[5] C. J. Campbell, A. G. Radnaev, A. Kuzmich, V. A. Dzuba, V. V. Flambaum, A. Derevianko, "Single-Ion nuclear clock for metrology at the 19th decimal place", Physical Review Letters, 108, 120802 (2012). Abstract.
[6] Marianna Safronova, "Nuclear physics: Elusive transition spotted in thorium", Nature, 533, 44-45 (2016). Abstract.
[7] Shimon Kolkowitz, Igor Pikovski, Nicholas Langellier, Mikhail D. Lukin, Ronald L. Walsworth, Jun Ye, "Gravitational wave detection with optical lattice atomic clocks", arXiv:1606.01859 [physics.atom-ph] (2016).
[8] V.V. Flambaum, "Enhanced effect of temporal variation of the fine structure constant and the strong interaction in ²²⁹Th", Physical Review Letters, 97, 092502 (2006). Abstract.
[9] B.R. Beck, J.A. Becker, P. Beiersdorfer, G.V. Brown, K.J. Moody, J.B. Wilhelmy, F.S. Porter, C.A. Kilbourne, R.L. Kelley, "Energy splitting of the ground-state doublet in the nucleus ²²⁹Th", Physical Review Letters, 98, 142501 (2007). Abstract.
[10] L.A. Kroger, C.W. Reich, "Features of the low energy level scheme of ²²⁹Th as observed in the alpha decay of ²³³U", Nuclear Physics A, 259, 29-60 (1976). Abstract.
[11] Ekkehard Peik, Maxim Okhapkin, "Nuclear clocks based on resonant excitation of gamma-transitions", Comptes Rendus Physique, 16, 516-523 (2015). Abstract.
[12] Lars von der Wense, Benedict Seiferle, Mustapha Laatiaoui, Jürgen B. Neumayr, Hans-Jörg Maier, Hans-Friedrich Wirth, Christoph Mokry, Jörg Runke, Klaus Eberhardt, Christoph E. Düllmann, Norbert G. Trautmann, Peter G. Thirolf, "Direct detection of the ²²⁹Th nuclear clock transition", Nature, 533, 47 (2016). Abstract.

A Continuously Pumped Reservoir of Ultracold Atoms

From Left to Right: (top row) Jan Mahnke, Ilka Kruse, Andreas Hüper, (bottom row) Wolfgang Ertmer, Jan Arlt, Carsten Klempt.

Authors: Jan Mahnke¹, Ilka Kruse¹, Andreas Hüper¹, Stefan Jöllenbeck¹, Wolfgang Ertmer¹, Jan Arlt², Carsten Klempt¹

Affiliation:
¹Institut für Quantenoptik, Gottfried Wilhelm Leibniz Universität Hannover, Germany
²Institut for Fysik og Astronomi, Aarhus Universitet, Aarhus C, Denmark

During the last decades, the quantum regime could be accessed through very different systems, including trapped ions, micromechanical oscillators, superconducting circuits and dilute ultracold gases. Mostly, these systems show the desired quantum-mechanical features at ultra-low temperatures only. The lowest temperatures [1] to date are reached in dilute atomic gases by a combination of laser cooling and evaporative cooling. This approach has two disadvantages: It relies on the internal structure of the atoms due to the laser cooling and it can only cool discrete samples instead of continuous beams due to the evaporative cooling.

However, many applications would greatly benefit from a continuous source of cold atoms, for example sympathetic cooling [2] of molecules. Here, the molecules are brought into contact with a bath of cold atoms to redistribute the thermal energy through collisions. Ideally, such a cold bath is realized in absence of disturbing laser light as the rich internal structure of the molecules results in a broad absorption spectrum and any photon can potentially harm the cooling process. Another application of a continuous beam of cold atoms is continuous matter interferometry. Atom interferometry is already in use for the precise measurement of many observables, including time [3], gravity [4] and rotation [5]. These measurements could greatly benefit from a continuous observation instead of the sequential interrogation of discrete samples. Even though continuous sources are highly desired, no continuous sources without the application of laser light have been demonstrated in the microkelvin regime yet.

One possible realization of an ultracold continuous sample was proposed theoretically [6], where a conservative and static trap is loaded by an atomic beam. In this scheme, pre-cooled atoms are guided towards the entrance barrier of an elongated trap with a finite trap depth (see figure 1). If the atoms pass the entrance barrier, they follow the elongated potential until they are reflected by the end of the trap. The strong confinement in the radial direction ensures that most atoms collide with another atom before they reach the entrance barrier again. These collisions allow for a redistribution of the kinetic energy. Consequently, some atoms acquire a kinetic energy larger than the trap depth and escape the trap. Other atoms lose energy and stay trapped. If the trap parameters are chosen well, an equilibrium condition with a surprisingly large phase-space density may be reached.

Figure 1: 3D plot of the static trapping potential in the x–z-plane through the point of the trap minimum.

In our recent publication [7], we demonstrate the first experimental implementation of such a continuous loading of a conservative trap. Our realization is based on a mesoscopic atom chip (see figure 2 and Ref. [8]), a planar structure of millimeter-sized wires. The mesoscopic chip generates the magnetic fields for a three-dimensional magneto-optical trap, a magnetic waveguide and the static trapping potential described above. The three-dimensional magneto-optical trap is periodically loaded with an ensemble of atoms. These ensembles are launched into the magnetic waveguide, where they overlap and produce a continuous atom beam with varying intensity. This beam traverses an aperture which optically isolates the loading region from the static trapping region. In this trapping region, the atom beam is directed onto the elongated magnetic trap, where the atoms accumulate.

Figure 2: Photograph of the mesoscopic atom chip with millimeter-scale wires. The magneto-optical trap is in the lower left area and the static trap is generated in the top right area. The bend wires create a guide connecting the two regions.

With this loading scheme, we create and maintain an atomic reservoir with a total number of 3.8 × 10⁷ trapped atoms at a temperature of 102 µK, corresponding to a peak phase-space density of 9 × 10^-8 h^-3. This is the first continuously loaded cloud in the microkelvin regime without the application of laser light. Such a continuously replenished ensemble of ultracold atoms presents a new tool for metrological tasks and for the sympathetic cooling of other atomic species, molecules or nanoscopic solid state systems. The scheme is also very versatile in creating cold samples of atoms and molecules directly, as it does not rely on any internal level structure.

Figure 3 Photograph of the experimental setup. The atom chip is visible outside of the vacuum chamber at the top. In the front is the glass cell and the optics for the two-dimensional magneto-optical trap, which is used to load the three dimensional magneto-optical trap on the chip.

References:
[1] A. E. Leanhardt, T. A. Pasquini, M. Saba, A. Schirotzek, Y. Shin, D. Kielpinski, D. E. Pritchard,  W. Ketterle. “Cooling Bose-Einstein condensates below 500 picokelvin”, Science, 301, 1513 (2003). Abstract.
[2] Wade G. Rellergert, Scott T. Sullivan, Svetlana Kotochigova, Alexander Petrov, Kuang Chen, Steven J. Schowalter, Eric R. Hudson, “Measurement of a large chemical reaction rate between ultracold closed-shell ⁴⁰Ca atoms and open-shell ¹⁷⁴Yb⁺ ions held in a hybrid atom-ion trap”, Physical Review Letters, 107, 243201 (2011). Abstract.
[3] R. Wynands and S. Weyers. “Atomic fountain clocks”, Metrologia, 42 (3), S64 (2005). Abstract.
[4] A. Louchet-Chauvet, S. Merlet, Q. Bodart, A. Landragin, F. Pereira Dos Santos, H. Baumann, G. D'Agostino, C. Origlia, “Comparison of 3 absolute gravimeters based on different methods for the e-MASS project”, Instrumentation and Measurement, IEEE Transactions on, 60(7), 2527-2532 (2011). Abstract.
[5] J. K. Stockton, K. Takase, and M. A. Kasevich. “Absolute geodetic rotation measurement using atom interferometry”, Physical Review Letters, 107, 133001 (2011). Abstract.
[6] C. F. Roos, P. Cren, D. Guéry-Odelin, and J. Dalibard. “Continuous loading of a non-dissipative atom trap”, Europhysics Letters, 61, 187 (2003). Abstract.
[7] J. Mahnke, I. Kruse, A. Hüper, S. Jöllenbeck, W. Ertmer, J. Arlt, C. Klempt. “A continuously pumped reservoir of ultracold atoms”, Journal of Physics B: Atomic Molecular and Optical Physics, 48, 165301 (2015). Abstract.
[8] S. Jöllenbeck, J. Mahnke, R. Randoll, W. Ertmer, J. Arlt, C. Klempt. “Hexapole-compensated magneto-optical trap on a mesoscopic atom chip”, Physical Review A, 83, 043406 (2011). Abstract.

Finding Optical Transitions for Testing a Fundamental Constant’s Constancy

From left to right: José, Alexander and Hendrik  discuss the spectral analysis -- standing next to the Heidelberg electron beam ion trap, where the results were obtained.

Authors: Alexander Windberger, Hendrik Bekker, José R. Crespo López-Urrutia

Affiliation: Max-Planck-Institut für Kernphysik, Heidelberg, Germany.

We studied the uncharted optical spectra of the highly charged ions W¹⁴⁺, Re¹⁵⁺, Os¹⁶⁺, Ir¹⁷⁺, and Pt¹⁸⁺, and demonstrated generally applicable methods to identify the measured spectral lines. That allowed us to infer the transition energies for proposed ultra-stable frequency standards using Hf¹²⁺ and W¹⁴⁺ ions. In Ir¹⁷⁺, optical transitions with the highest sensitivity to a potential variation of the fine structure constant α ever predicted for a stable atomic system were determined. Highly advanced atomic structure calculations were benchmarked in the extreme regime of a triple level crossing.

Fundamental constants are taken as given by Nature. Our understanding of the origin of these constants is, however, rather poor: Their values are not set within the Standard Model but have to be determined empirically. Alternative theories, such as string or coupled dark energy theories, assume that fundamental constants emerge from dynamical fields and can vary at different times or places in the universe (see [1] for a review). Therefore, probing the stability of these constants allows us to search for physics beyond the Standard Model.

Our work focusses on testing a possible variation of the fine structure constant α, which characterizes the strength of interaction between charged particles and photons. Very small variations of α would lead to a detectable shift of wavelength, or color, of light which is emitted or absorbed by atoms. Following this approach the group of Webb et al. obtained the absorption spectra of interstellar clouds billions of light years away from us and in an extensive analysis found wavelength shifts for spectra observed at different angles [2]. This was interpreted as a spatial dipole-like variation of α.

We aim to test this extraordinary claim under well-defined laboratory conditions, preventing systematic uncertainties that the astrophysical observations might suffer from. Since the Earth, the Solar System, and our galaxy all move, a spatial variation translates into an effective temporal variation which was estimated at 10^-19/year [3]. Such a minuscule drift could be measured by monitoring the frequency ratio of two highly accurate optical atomic clocks. The clock transitions should be very sensitive to an α variation, but to nothing else. Highly charged ions fulfill these requirements. With an increasing ionic charge, the wavelengths of electronic transitions decrease and leave the range accessible to lasers. Systems with level crossings are an exception. When two or more configurations are almost equal in energy, optical transitions are possible. The level crossing of the 5s and 4f subshells predicted for Ir¹⁷⁺ should enable the highest sensitivity to the sought-after α variation in a stable atomic system [4].

No detailed knowledge of the electronic structure of these ion species existed. Most heavy highly charged ions, as Ir¹⁷⁺, are experimentally unexplored, and calculations are not sufficiently accurate for these complex systems. For our studies, we used the Heidelberg electron beam ion trap, which produces and traps the ions of interest. The continuously excited ions decay by emitting radiation, of which we analyzed the optical spectrum. An exemplary measurement can be seen in Fig. 1, showing the optical spectra of W¹⁴⁺, Re¹⁵⁺, Os¹⁶⁺, Ir¹⁷⁺, and Pt¹⁸⁺ (atomic numbers Z=74-78). These ions encompass the whole predicted 5s-4f level crossing region.

Figure 1. (Click on the figure to view with higher resolution) Typical spectral map of Ir ions measured using the Heidelberg electron beam ion trap. For this measurement we acquired spectra at 10 V intervals of the electron beam acceleration potential. New groups of fluorescence lines start to appear when the electron beam energy reaches the ionization potential of an ionic charge state. The new charge state is produced more efficiently as the electron beam energy further increases, and the fluorescence lines become stronger until the ionization threshold of the next higher charge state is reached. At this point the ion population is transferred to the next charge state, which starts to fluoresce, while the former one disappears. This dependence of the fluorescence intensity on the acceleration potential is depicted in the right graph. It is notable that this section of the optical spectrum assigned to Ir¹⁷⁺ already shows a dense manifold of spectral lines. In order to derive the level structure from the spectrum, sophisticated identification schemes had to be applied.

Subsequently, we assigned the measured spectral lines to their corresponding electronic transitions to establish the level scheme [5]. Given the large theoretical uncertainties, a direct comparison of calculated and measured spectra is futile. Instead, we used three alternative methods to identify the spectral lines.

First, we exploited the fact that these ions are isoelectronic, since they have the same number of electrons, and thus similar atomic structures. Over a limited range of atomic numbers, the transition energies depend on the respective nuclear charge with a simple polynomial scaling. By comparison between the measured scaling functions and theoretical predictions we were able to reliably identify all underlying transitions as can be seen in Fig. 2.

Figure 2. (Click on the figure to view with higher resolution) Identification of isoelectronic transitions using their characteristic energy scaling. (a) Measured spectra of W¹⁴⁺, Re¹⁵⁺, Os¹⁶⁺, Ir¹⁷⁺, and Pt¹⁸⁺ (black lines). An algorithm found nine isoelectronic transition energies that obey simple quadratic scaling laws (colored lines) as expected from theoretical considerations. (b) By comparing the experimentally determined constant offset A and the linear term B (full symbols) to the calculated ones (open symbols) an unambiguous identification of the underlying transitions could be achieved.

This method could be independently confirmed by measuring the identified transitions in Ir¹⁷⁺ with increased resolution and accuracy. The spectral lines revealed a characteristic line shape caused by the 8 T magnetic field present at the position of the trapped ions. The observed line shapes were individually modelled according to the Zeeman effect, leading to an independent verification in perfect agreement with the scaling method.

The identified transitions allowed us to test advanced atomic structure calculations for the first time in systems with such a complex level crossing of 4f ¹² 5s², 4f¹³ 5s, and 4f ¹⁴ configurations. We found that only relativistic multi-reference Fock-space coupled cluster calculations consistently showed a fair agreement with most of the observed lines.

A direct application is the determination of the transition energies of two proposed optical clock transitions with a potential relative frequency uncertainty of less than 10^-19 in W¹⁴⁺ and Hf¹²⁺ [6], another isoelectronic ion. Although we did not measure the spectrum of Hf¹²⁺, we were able to extrapolate the transition energy by applying the established energy scaling. Our experimental uncertainty is at least one order of magnitude smaller than that of predictions.

These clock transitions are exceptionally stable. However, they are not sensitive to a variation of the fine structure constant. For that, Ir¹⁷⁺ is ideal. By searching our data, we found closed transition cycles (Rydberg-Ritz principle) combining the identified with unidentified transitions. This enabled us to find two possible, but mutually excluding, candidates for the proposed α-sensitive transitions. We are currently performing more accurate measurements to remove this ambiguity.

Our method, line assignments by isoelectronic scaling of transitions (LINE ASSIST) is a straight-forward and general tool for exploring unknown spectra of highly charged ions. With the recent successful application of sympathetic cooling to highly charged ions [7], much higher accuracy can be achieved in future work: the ion temperature was reduced by nearly six orders of magnitude and the Doppler width accordingly. The experimental values for the transition energies obtained in the present work are needed for follow-up laser spectroscopy studies, applications as optical clock transitions, and testing the constancy of fundamental constants.

References:
[1] Jean-Philippe Uzan, "The fundamental constants and their variation: observational and theoretical status". Review of Modern Physics, 75, 403–455 (2003). Abstract.
[2] J. K. Webb, J. A. King, M. T. Murphy, V. V. Flambaum, R. F. Carswell, M. B. Bainbridge, "Indications of a Spatial Variation of the Fine Structure Constant". Physical Review Letters, 107, 191101 (2011). Abstract.
[3] J.C. Berengut, V.V. Flambaum, "Manifestations of a spatial variation of fundamental constants in atomic and nuclear clocks, Oklo, meteorites, and cosmological phenomena". Europhysics Letters, 97, 20006 (2012). Abstract.
[4] J.C. Berengut, V.A. Dzuba, V.V. Flambaum, A. Ong, "Electron-Hole Transitions in Multiply Charged Ions for Precision Laser Spectroscopy and Searching for Variations in α". Physical Review Letters, 106, 210802 (2011). Abstract.
[5] A. Windberger, J.R. Crespo López-Urrutia, H. Bekker, N.S. Oreshkina, J.C. Berengut, V. Bock, A. Borschevsky, V.A. Dzuba, E. Eliav, Z. Harman, U. Kaldor, S. Kaul, U.I. Safronova, V.V. Flambaum, C.H. Keitel, P.O. Schmidt, J. Ullrich, O.O. Versolato, "Identification of the Predicted 5s−4f  Level Crossing Optical Lines with Applications to Metrology and Searches for the Variation of Fundamental Constants". Physical Review Letters, 114, 150801 (2015). Abstract.
[6] V. A. Dzuba, A. Derevianko, V.V. Flambaum, "High-precision atomic clocks with highly charged ions: Nuclear-spin-zero f ¹²-shell ions". Physical Review A, 86, 054501 (2012). Abstract.
[7] L. Schmöger, O.O. Versolato, M. Schwarz, M. Kohnen, A. Windberger, B. Piest, S. Feuchtenbeiner, J. Pedregosa-Gutierrez, T. Leopold, P. Micke, A.K. Hansen, T.M. Baumann, M. Drewsen, J. Ullrich, P.O. Schmidt, J.R. Crespo López-Urrutia, "Coulomb crystallization of highly charged ions". Science, 347, 1233 (2015). Abstract.

Quantum Information in the Service of Metrology

The spin-spin measurement team at Weizmann Institute of Science, Israel. From left-to-right: Nir Navon, Nitzan Akerman, Roee Ozeri, Shlomi Kotler and Yinnon Glickman

Authors: Roee Ozeri¹, Shlomi Kotler^1,2

Affiliation:
¹Department of Physics of Complex Systems, Weizmann Institute of Science, Israel.
²Current address: Physical measurement Laboratory, National Institute of Standards and Technology, Boulder, USA.

Quantum systems have been extensively studied in the past few years as possible ultra-efficient computers. Such systems have to be as isolated as possible from their environment in order to prevent it from “measuring” the state of the quantum computer, a process which would render the computer classical. Candidate systems that were experimentally studied thus had to be sufficiently isolated from their environment while allowing for a high degree of controllability.

In addition, active methods were developed, in which special quantum states and control techniques were engineered and helped mitigate the effect of noise. Many such techniques, such as dynamic-decoupling or decoherence-free subspaces, were experimentally implemented with great success, increasing the coherence times of quantum systems by many orders of magnitude. Other methods, such as Quantum error-correction codes, have had proof-of principle demonstrations but hold the promise of being able to reject noise in a way where quantum super-positions of very large systems will be maintained coherent for as long as necessary – one of the key requirement from a quantum computer.

A different quantum technology which has seen great progress in recent years is that of quantum metrology. At face value, quantum sensors seem to be exactly antipodal to quantum computers. Here, quantum systems do have to couple to their environment in order to sense some aspect of it. However, as in many seemingly contradicting concepts there can also be a lot of common ground. For example, environmental noise (i.e. that part of the environment which you don’t want to measure!) is a foe of both quantum sensors and quantum computers. Can we therefore use the techniques that were developed to help quantum computers overcome the harmful effects of noise to improve on the measurement precision of quantum sensors? The answer is yes, and with great success! Along these lines, different dynamic modulations schemes, originally used in dynamic decoupling were used for the measurement of alternating signals. This way quantum lock-in amplifiers as well as quantum noise spectrum analyzers were demonstrated. In a recent experiment in our lab at the Weizmann Institute of Science, we used the powerful technique of decoherence-free subspaces in order to measure the very weak magnetic interaction between two electrons that were separated by more than two microns [1].

Figure 1: An artist impression of the spin-spin experiment. Two electrons are placed two microns away from each other. The magnetic field emanating from one electron interacts with the spin of the other electron, resulting in a change of the spin-orientations.

Electrons, like many fundamental particles have an intrinsic magnetic dipole moment which is aligned with their spin. These tiny magnets have a magnetic field that decays as the cube of the distance from the electron. To illustrate, the magnetic field of a single electron two microns away from it, is as small as the earths’ magnetic field at 10 times the distance to the moon. When two electrons feel each other’s magnetic fields their spins interact as magnets do: their opposite poles will attract, their identical poles repel in a way that torques will be applied and the two spins will respectively rotate due to this interaction.

The magnetic interaction between two electrons was never directly observed before. At short atomic distances, such as that between the two electrons of a Helium atom, the magnetic interaction is large enough to be easily measured. Unfortunately, at these distances, it is overwhelmed by the much larger exchange interaction between them which is the result of the interplay between the strong Coulomb interaction between the electron charges and Fermi’s exclusion principle. At large distances, where the exchange interaction is negligible, the magnetic interaction between the electrons is also very small. At a distance of two microns for example, the rotation rate the two spins impose on each other is on the order of one rotation every four minutes. This interaction is way too small to be measured due to typical magnetic noise in labs.

Figure 2: An image of the trap in which the ions were trapped for the duration of the measurement. The image is taken through one of the ultra-high vacuum chamber view-ports.

This is where techniques, borrowed from quantum computing science come to the rescue. We have placed the spins of two trapped Sr+ ions in a decoherence-free subspace that was completely immune to the effect of magnetic field noise. While being immune to noise, this subspace still allowed for the slow and gentle two-spin correlated dance to be performed without interference. Under the protection provided by this technique we could allow the electronic spins to rotate coherently for 15 seconds, after which we measured their collective rotation of more than 20^◦. We also changed the distance between the electrons and verified that the interaction between them varies inverse cubical with their separation. Thus, almost a 100 years after the discovery of the electronic spin, we were able to cleanly observe the interaction between two such tiny magnets.

This measurement bears importance that reaches beyond its demonstrative nature. This is because some hypothetical anomalous spin forces are speculated to modify the interaction between electronic spins at large distances. The motivation for the introduction of these anomalous forces is due to their ability to explain the weakness with which certain symmetries are broken in nature. The experimental bound on the strength and range of these hypothetical fields is therefore important.

The use of quantum error-suppression schemes for the benefit of precision measurements is a fast developing area of research. With the advent of experimental quantum error-correction codes, another opportunity will emerge to apply these codes towards the detection of small and highly correlated signals [2-5].

References:
[1] Shlomi Kotler, Nitzan Akerman, Nir Navon, Yinnon Glickman, Roee Ozeri, "Measurement of the magnetic interaction between two bound electrons of two separate ions". Nature, 510, 376 (2014). Abstract.
[2] Roee Ozeri, "Heisenberg limited metrology using Quantum Error-Correction Codes". arXiv:1310.3432 [quant-ph].
[3] G. Arrad, Y. Vinkler, D. Aharonov, A. Retzker, "Increasing Sensing Resolution with Error Correction". Physical Review Letters, 112, 150801 (2014). Abstract.
[4] E. M. Kessler, I. Lovchinsky, A. O. Sushkov, M. D. Lukin, "Quantum Error Correction for Metrology". Physical Review Letters, 112, 150802 (2014). Abstract.
[5] W. Dür, M. Skotiniotis, F. Fröwis, B. Kraus, "Improved Quantum Metrology Using Quantum Error Correction". Physical Review Letters, 112, 080801 (2014). Abstract.

Comparing Matter Waves in Free Fall

[From Left to Right] J. Hartwig, D. Schlippert, E. M. Rasel

Authors: J. Hartwig, D. Schlippert, Ernst M. Rasel

Affiliation: Institut für Quantenoptik and Centre for Quantum Engineering and Space-Time Research (QUEST), Leibniz Universität Hannover, Germany

Introduction to Einstein’s Equivalence Principle

Einstein’s general relativity is based on three fundamental building blocks: local Lorentz invariance, the universality of the gravitational redshift and the universality of free fall. The enormous importance of general relativity in modern science and technology merits a continuous effort in improving experimental verification of these underlying principles.

The universality of free fall is one of the oldest mechanical theories originally proposed by Galileo. Testing can be done by so called free fall experiments, where two bodies with different composition are freely falling towards a third gravitating body.

Figure 1: Goddard Spaceflight Center Laser Ranging Facility. Source: NASA

Amongst the most sensitive measurements of this principle is the Lunar Laser Ranging experiment, which compares the free fall of earth and moon in the solar gravitational potential [1]. This measurement is only surpassed by torsion balance experiments based on the design of Eötvös [2]. In addition, exciting new insights are expected from the MICROSCOPE experiment [3] that is planned to launch in 2016.

Figure 2: Torsion balance experiment as used in the group of E. Adelberger, University of Washington. Source: Eöt-Wash-Group

The emergence of quantum physics and our improved understanding of the basic building blocks of matter increases the interest scientists have in the understanding of gravity. How do gravity and quantum mechanics interact? What`s the connection between different fundamental particles and their mass? Is there a deeper underlying principle combining our fundamental theories? To comprehensively approach these questions a wide array of parameters must be analyzed. The way how certain test materials may act under the influence of gravity can either be parametrized using a specific violation scenario, like the Dilaton scenario by T. Damour [4], or by using a test theory such as the extended Standard Model of particles (SME) [5]. Since the SME approach is not based on a specific mechanism of violating UFF it also does not predict a level to which a violation may occur. Instead, it delivers a model-independent approach to compare methodically different measurements and confine possible violation theories.

Table 1 states possible sensitivities for violations based on the SME framework for a variety of test masses and underlines the importance of complementary test mass choices are. Hence in comparison to classical tests, the use of atom interferometry opens up a new field of previously inaccessible test masses with perfect isotopic purity in a well-defined spin state. Quantum tests appear to differ from previous test also in a qualitative way. They allow to perform test with new states of matter, such as wave packets by Bose Einstein condensates being in a superposition state. The work presented here is just another early step in a quest to understand the deeper connections between the quantum and classical relativistic world.

Table 1: Sample violation strengths for different test masses linked to “Neutron excess” and the “total Baryon number” based on the Standard Model Extension formalism. The test mass pairs are chosen according to the best torsion balance experiment [6] and existing matter wave tests [7]. An anomalous acceleration would be proportional to the stated numerical coefficients. Source: D. Schlippert et al., Phys. Rev. Lett. 112, 203002 (2014).

Measuring accelerations with atom interferometry

Measuring accelerations with a free fall experiment is always achieved by tracking the movement of an inertial mass in free fall in comparison to the lab frame of reference. This is even true when the inertial mass in question needs to be described by a matter wave operating on quantum mechanics. Falling corner cube interferometers operating on this principle are among the most accurate measurements of gravity with classical bodies. They use a continuous laser beam to track the change of velocity of a corner cube reflector due to gravity in a Michelson interferometer with the corner cube changing one of the arm lengths. Acceleration sensors based on free falling matter waves use a similar principle.

Figure 3: A side view of the experimental setup with the two-dimensional (left side) and three-dimensional (right side) magneto-optical traps employed in [Phys. Rev. Lett. 112, 203002 (2014)].

The first demonstration of a true quantum test of gravity with matter waves was performed 1975 with neutrons in the Famous COW experiment [8]. We will focus on atom interferometers using alkaline atoms, since they are most commonly used for inertial sensing and are also employed in the discussed experiment. Experiments of this kind were first used for acceleration measurements in 1992 [9] and have improved in their performance ever since. The first test of the equivalence principle comparing two different isotopes was then performed in 2004 [10]. Research on quantum tests is for example proposed at LENS in Italy [11], in Stanford in an already existing large fountain [12] and in the scope of the French ICE mission in a zero-g plane [13]. All these initiatives show the high interest of testing gravity phenomena with quantum matters as opposed to classical tests.

In the case of atom interferometers, coherent beam splitting is performed by absorption and stimulated emission of photons. Which atomic transitions are used is dependent on the specific application but, in the case of alkaline atoms two photon transitions coupling either two hyperfine and respective momentum states (Raman transitions) or just momentum states (Bragg transitions) are employed. The point of reference for the measurement is then given by a mirror reflecting the laser beams used to coherently manipulate the atoms, since the electromagnetic field is vanishing at the mirror surface. This results in a reliable phase reference of the light fields and constitutes the laboratory frame. The role of the retroreflecting mirror is similar to the one of the mirror at rest in in the case of the falling corner cube experiment.

The atomic cloud acts as the test mass, which in an ideal case, is falling freely without any influence by the laboratory, except during interaction with the light fields employed as beam splitters or mirrors. During the interaction, the light fields drive Rabi-oscillations in the atoms between the two interferometer states |g> and |e> with a time 2τ needed for a full oscillation. This allows for the realization of beam splitters with a τ/2 pulse length resulting in an equal superposition of |g> and |e>. Mirrors can be realized the same way by applying the beam splitter light fields for a time of τ which leads to an inversion of the atomic state. These pulses are generally called π/2 (for the superposition) and π (for the inversion pulses) in accordance with the Rabi-oscillation phase. The simplest geometry used to measure acceleration is a Mach- Zehnder-like geometry. This is produced by applying a π/2-π-π/2 sequence with free evolution times T placed between pulses. The resulting geometry can be seen in Figure 4.

Figure 4: Space-time diagram of a Mach-Zehnder-like atom interferometer. An atomic ensemble is brought into a coherent superposition of two momentum states by a stimulated Raman transition (π/2 pulse). The two paths I+II propagate separated, are reflected by a pi-pulse after a time T and superimposed and brought to interference with a final π/2 pulse after time 2T. The phase difference is encoded in the population difference of the two output states.

During the interaction with the light fields, the lattice formed by the two light fields imprints its local phase onto the atoms. This results in an overall phase scaling with the relative movement between the atomic cloud and the lattice. Calculating the overall phase imprinted on the atoms results in first order term, Φ=a*T²*k_eff, where k_eff is the effective wave vector of the lattice and a is the relative acceleration between lattice and atoms. This immediately shows the main feature of free fall atom interferometry: the T² scaling of the resulting phase. This is of particular interest for future experiments aiming for much higher free evolution times than currently possible. The phase Φ also shows another key feature. As the acceleration between atoms and lattice approaches zero, the phase also goes to zero, independently of the interferometry time T. This yields a simple way to determine the absolute acceleration of the atomic sample by accelerating the lattice until the lattice motion is in the same inertial reference frame as the freely falling atoms.

Lattice acceleration is achieved by chirping the frequency difference between the two laser beams used for the two photon transition. This transforms the measurement of a relatively large phase, spanning many thousand radians, to a null measurement. The signal produced is the population difference between the interferometer states |g> and |e> as a function of lattice acceleration and thus frequency sweep rate, α. The sweep rate corresponding to a vanishing phase directly leads to the acceleration experienced by the atoms according to lattice acceleration formula a=α/k_eff. Taking into account Earth’s gravitational field and a lattice wavelength of 780/2 nm (the factor of ½ is introduced due to the use of a two-photon transition) this leads to a sweep rate of around 25 MHz/s. The advantage of this method is that the acceleration measurement is now directly coupled to measurement of the wavelength of the light fields and frequencies in the microwave regime, which are easily accessible.

Our data

Figure 5: Determination of the differential acceleration of rubidium and potassium. The main systematic bias contributions do not change their sign when changing the direction of momentum transfer. Hence, the mean acceleration of upward and downward momentum transfer direction greatly suppresses the aforementioned biases. Source: D. Schlippert et al., Phys. Rev. Lett. 112, 203002 (2014)

Figure 6:  the wave nature of ⁸⁷Rb and ³⁹K 
atoms and their interference are exploited 
to measure the gravitational acceleration.

In order to test the universality of free fall, we simultaneously chirp the Raman frequencies to compensate for the accelerations a(Rb,±)(g) and a(K,±)(g) experienced by rubidium and potassium that were previously identified (Figure 6). Here, the observed phase shift exhibits contributions due to additional perturbations, such as magnetic field gradients. We make use of a measurement protocol based on reversing the transferred momentum (upward and downward directions ±). This technique makes use of the fact that many crucial perturbations do not depend on the direction of momentum transfer. Thus, by computing the half-difference of the phase differences determined in a single momentum direction, phase shifts induced by, e.g., the AC-Stark effect or Zeeman effect, can be strongly suppressed [14].

Figure 7: Allan deviations of the single species interferometer signals and the derived Eötvös ratio. Source: D. Schlippert et al., Phys. Rev. Lett. 112, 203002 (2014)

The data presented in this work [15] was acquired in a data run that was ~4 hours long. By acquiring 10 data points per direction of momentum transfer, and species and then switching to the opposite direction, we were able to determine the Eötvös ratio of rubidium and potassium to a statistical uncertainty of 5.4 x 10^-7 after 4096s; the technical noise affecting the potassium interferometer is the dominant noise source.

Taking into account all systematic effects, our measurement yields η(Rb,K)=(0.3 ± 5.4) x 10^-7.

Outlook

In our measurement, the performance was limited both by technical noise and the limited free evolution time T. In order to improve these parameters, we are currently extending the free fall time in our experiment. Furthermore, in an attempt to increase the contrast of our interferometers and thus the signal-to-noise ratio, we are working on implementing state preparation schemes for both species.

We expect to constrain our uncertainty budget (which currently is on the 10 ppb level for the Eötvös ratio) on the ppb level and below through the use of a common optical dipole trap applied to both species. By using Bose-Einstein-condensed atoms, we gain the ability to precisely calculate the ensembles, as well as carefully control the input state. This technique will also be able to reduce uncertainty factors linked to the transverse motion of the cloud, in addition to spatial magnetic field and gravitational field gradients.

Improving the precision of a true quantum test into the sub-ppb regime is the focus of current research. For example we are currently planning a 10m very long baseline atom interferometer (VLBAI) in Hannover [16]. In the framework of projects funded by the German Space Agency (DLR), we moreover develop experiments that are suitable for microgravity operation in the ZARM drop tower in Bremen and on sounding rocket missions [17].

Parallel to the development done in the LUH and at a national level, we are also involved in projects on an international level looking into extending the frontier of atom interferometry and especially the test of the equivalence principle. A major project investigating the feasibility of a space borne mission is the STE-Quest Satellite Mission proposed by a European consortium including nearly all major research institutions working in the field of inertial sensing with atom interferometry, as well as a variety of specialist of other fields [18]. This mission is aimed towards doing a simultaneous test of the equivalence principle with two rubidium isotopes and a clock comparison with several ground based optical clocks, pushing the sensitivity to the Eötvös ratio into the 10^-15 regime.

References:
[1] James G. Williams, Slava G. Turyshev, Dale H. Boggs, "Progress in Lunar Laser Ranging Tests of Relativistic Gravity". Physical Review Letters, 93, 261101 (2004). Abstract.
[2] S. Schlamminger, K.-Y. Choi, T. A. Wagner, J. H. Gundlach, E. G. Adelberger, "Test of the Equivalence Principle Using a Rotating Torsion Balance". Physical Review Letters, 100, 041101 (2008). Abstract.
[3] P. Touboul, G. Métris, V. Lebat, A Robert, "The MICROSCOPE experiment, ready for the in-orbit test of the equivalence principle". Classical and Quantum Gravity, 29, 184010 (2012). Abstract.
[4] Thibault Damour, "Theoretical aspects of the equivalence principle". Classical Quantum Gravity, 29, 184001 (2012). Abstract.
[5] M.A. Hohensee, H. Müller, R.B. Wiringa, "Equivalence Principle and Bound Kinetic Energy". Physical Review Letters, 111, 151102 (2013). Abstract.
[6] S. Schlamminger, K.-Y. Choi, T.A. Wagner, J.H. Gundlach, E.G. Adelberger, "Test of the Equivalence Principle Using a Rotating Torsion Balance". Physical Review Letters, 100, 041101 (2008). Abstract.
[7] A. Bonnin, N. Zahzam, Y. Bidel, A. Bresson, "Simultaneous dual-species matter-wave accelerometer". Physical Review A, 88, 043615 (2013). Abstract ; S. Fray, C. Alvarez Diez, T. W. Hänsch, M. Weitz, "Atomic Interferometer with Amplitude Gratings of Light and Its Applications to Atom Based Tests of the Equivalence Principle". Physical Review Letters, 93, 240404 (2004). Abstract ; M. G. Tarallo, T. Mazzoni, N. Poli, D. V. Sutyrin, X. Zhang, G. M. Tino, "Test of Einstein Equivalence Principle for 0-Spin and Half-Integer-Spin Atoms: Search for Spin-Gravity Coupling Effects". Physical Review Letters, 113, 023005 (2014). Abstract.
[8] R. Colella, A. W. Overhauser, S. A. Werner, "Observation of Gravitationally Induced Quantum Interference". Physical Review Letters, 34, 1472 (1975). Abstract.
[9] M. Kasevich, S. Chu, "Measurement of the gravitational acceleration of an atom with a light-pulse atom interferometer". Applied Physics B, 54, 321–332 (1992). Abstract.
[10] Sebastian Fray, Cristina Alvarez Diez, Theodor W. Hänsch, Martin Weitz, "Atomic Interferometer with Amplitude Gratings of Light and Its Applications to Atom Based Tests of the Equivalence Principle". Physical Review Letters, 93, 240404 (2004). Abstract.
[11] M. G. Tarallo, T. Mazzoni, N. Poli, D. V. Sutyrin, X. Zhang, G. M. Tino, "Test of Einstein Equivalence Principle for 0-Spin and Half-Integer-Spin Atoms: Search for Spin-Gravity Coupling Effects". Physical Review Letters, 113, 023005 (2014). Abstract.
[12] Susannah M. Dickerson, Jason M. Hogan, Alex Sugarbaker, David M. S. Johnson, Mark A. Kasevich, "Multiaxis Inertial Sensing with Long-Time Point Source Atom Interferometry". Physical Review Letters, 111, 083001 (2013). Abstract. 2Physics Article.
[13] G Varoquaux, R A Nyman, R Geiger, P Cheinet, A Landragin, P Bouyer, "How to estimate the differential acceleration in a two-species atom interferometer to test the equivalence principle". New Journal of Physics, 11, 113010 (2009). Full Article.
[14] J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and,M. A. Kasevich, "Sensitive absolute-gravity gradiometry using atom interferometry". Physical Review A, 65, 033608 (2002). Abstract; Anne Louchet-Chauvet, Tristan Farah, Quentin Bodart, André Clairon, Arnaud Landragin, Sébastien Merlet, Franck Pereira Dos Santos, "The influence of transverse motion within an atomic gravimeter". New Journal of Physics, 13, 065025 (2011). Full Article.
[15] D. Schlippert, J. Hartwig, H. Albers, L. L. Richardson, C. Schubert, A. Roura, W. P. Schleich, W. Ertmer, E. M. Rasel, "Quantum Test of the Universality of Free Fall". Physical Review Letters, 112, 203002 (2014). Abstract.
[16] http://www.geoq.uni-hannover.de/350.html
[17] http://www.iqo.uni-hannover.de/quantus.html
[18] D N Aguilera, H Ahlers, B Battelier, A Bawamia, A Bertoldi, R Bondarescu, K Bongs, P Bouyer, C Braxmaier, L Cacciapuoti, C Chaloner, M Chwalla, W Ertmer, M Franz, N Gaalou, M Gehler, D Gerardi, L Gesa, N Gürlebeck, J Hartwig, M Hauth, O Hellmig, W Herr, S Herrmann, A Heske, A Hinton, P Ireland, P Jetzer, U Johann, M Krutzik, A Kubelka, C Lämmerzah, A Landragin, I Lloro, D Massonnet, I Mateos, A Milke, M Nofrarias, M Oswald, A Peters, K Posso-Trujillo, E Rase, E Rocco, A Roura, J Rudolph, W Schleich, C Schubert, T Schuldt, S Seide, K Sengstock, C F Sopuerta, F Sorrentino, D Summers, G M Tino, C Trenkel, N Uzunoglu, W von Klitzing, R Walser, T Wendrich, A Wenzlawski, P Weßels, A Wicht, E Wille, M Williams, P Windpassinger, N Zahzam,"STE-QUEST—test of the universality of free fall using cold atom interferometry". Classical Quantum Gravity, 31, 115010 (2014), Abstract.

Entanglement-enhanced Atom Interferometer with High Spatial Resolution

(From left to right) Philipp Treutlein, Roman Schmied, and Caspar Ockeloen

Authors: Caspar Ockeloen, Roman Schmied, Max F. Riedel, Philipp Treutlein

Affiliation: Department of Physics, University of Basel, Switzerland

Link to Quantum Atom Optics Lab, Treutlein Group >>

Interferometry is the cornerstone of most modern precision measurements. Atom interferometers, making use of the wave-like nature of matter, allow for ultraprecise measurements of gravitation, inertial forces, fundamental constants, electromagnetic fields, and time [1,2]. A well-known application of atom interferometry is found in atomic clocks, which provide the definition of the second. Most current atom interferometers operate with a large number of particles, which provides high precision but limited spatial resolution. Using a small atomic cloud as a scanning probe interferometer would enable new applications in electromagnetic field sensing, surface science, and the search for fundamental short-range interactions [2].

Past 2Physics article by Philipp Treutlein:
May 09, 2010: "Interface Between Two Worlds -- Ultracold atoms coupled to a micromechanical oscillator"
by Philipp Treutlein, David Hunger, Stephan Camerer.

In an atom interferometer, the external (motional) or internal (spin) state of atoms is coherently split and allowed to follow two different pathways. During the interrogation time T, a phase difference between the paths is accumulated, which depends on the quantity to be measured. When the paths are recombined, the wave-character of the atoms gives rise to an interference pattern, from which the phase can be determined. To measure this interference, the number of atoms in each output state is counted. Here the particle-character of the atoms is revealed, as the measurement process randomly projects the wave function of each atom into a definite state. When operating with an ensemble of N uncorrelated (non-entangled) atoms, the binomial counting statistics limits the phase uncertainty of the interferometer to 1/√N, the standard quantum limit (SQL) of interferometric measurement.

It is possible to overcome the SQL by making use of entanglement between the atoms [3]. Using such quantum correlations, the measurement outcome of each atom can depend on that of the other atoms. If used in a clever way, the phase uncertainty of an interferometer can be reduced below the SQL, in theory down to the ultimate Heisenberg limit of 1/N. Such entanglement-enhanced interferometry is in particular useful in situations where the number of atoms is limited by a physical process and the sensitivity can no longer be improved by simply increasing N. One such scenario is when high spatial resolution is desired. The number of atoms in a small probe volume is fundamentally limited by density-dependent losses due to collisions. As more atoms are added to this volume, the collision rate increases, and eventually any additional atoms are simply lost from the trap before the interferometer sequence has completed. This sets a tight limit on both the phase uncertainty and the maximum interrogation time T.

Fig. 1. Experimental setup. a) Central region of the atom chip showing the atomic probe (blue, size to scale) and the scanning trajectory we use. The probe is used to measure the magnetic near-field potential generated by an on-chip microwave guide (microwave currents indicated by arrows). A simulation of the potential is shown in red/yellow. b) Photograph of the atom chip, mounted on its ultra-high vacuum chamber.

In a recent paper [4] we have demonstrated a scanning-probe atom interferometer that overcomes the SQL using entanglement. Our interferometer probe is a Bose-Einstein condensate (BEC) on an atom chip, a micro-fabricated device with current-carrying wires that allow magnetic trapping and accurate positioning of neutral atoms close to the chip surface [5]. A schematic view of the experiment is shown in figure 1. We use N=1400 Rubidium-87 atoms, trapped in a cloud of 1.1 x 1.1 x 4.0 micrometers radius, 16 to 40 micrometers from the surface. Two internal states of the atoms are used as interferometric pathways, and the pathways are split and recombined using two-photon microwave and radio frequency pulses. At the end of the interferometer sequence, we count the atoms in each output state with sensitive absorption imaging, with a precision of about 5 atoms.

We create entanglement between the atoms by making use of collisions naturally present in our system. When two atoms collide, both atoms obtain a phase shift depending on the state of the other atom, thus creating quantum correlations between the two. Normally, the effect of these collisions is negligible in our experiment, as the phase shift due to collisions between atoms in the same state are almost completely canceled out by collisions where each atom is in a different state. We can turn on the effect of collisions by spatially separating the two states, such that collisions between states do not occur. When, after some time, we recombine the two states, collisional phase shifts are effectively turned off during the subsequent interrogation time of the interferometer.

The performance of our interferometer is shown in figure 2, measured at 40 micrometer from the chip surface. It has a sensitivity of 4 dB in variance below to SQL, and improved sensitivity is maintained for up to T = 10 ms of interrogation time, longer than in previous experiments [6,7,8]. We demonstrate the scanning probe interferometer by transporting the entangled atoms between 40 and 16 micrometer from the atom chip surface, and measuring a microwave near field potential at each location. The microwave potential is created by wires on our atom chip, and is also used for generation of the entangled state. As shown in figure 3, our scanning probe interferometer operates on average 2.2 dB below the SQL, demonstrating that the entanglement partially survives being transported close to the chip surface, which takes 20 ms of transport time.

Fig. 2. Interferometer performance operating at a single position for different interrogation times. Plotted is the variance relative to the standard quantum limit (SQL). The entanglement-enhanced interferometer (blue diamonds) operates about 4 dB below the SQL, whereas the non-entangled interferometer (red, coherent state) operates close to the SQL. For T > 10 ms, both experiments are limited by technical noise. The inset shows a typical interference fringe, with a fringe contrast of (98.1 ± 0.2)%.

The scanning probe measurement presented here corresponds to a microwave magnetic field sensitivity of 2.4 µT in a single shot of the experiment (cycle time ~ 11 s). The sensitivity shown in figure 2 corresponds to 23 pT for an interrogation time of 10 ms. This sensitivity is obtained with a probe volume of only 20 µm³. Our interferometer bridges the gap between vapor cell magnetometers, which achieve subfemtotesla sensitivity at the millimeter to centimeter scale [9,10] but do not have the spatial resolution needed to resolve near-field structures on microfabricated devices, and nitrogen vacancy centers in diamond, which are excellent magnetometers at the nanometer scale but currently offer lower precision in the micrometer regime [11].

Fig. 3. Scanning probe interferometer. a) Phase shift due to the microwave near-field potential measured at different positions. The dashed line is a simulation of the potential. b) Interferometer performance for the same measurement. At all positions, the interferometer operates below the SQL. These measurements were done with an interrogation time of T = 100 µs, during which the microwave near-field was pulsed on for 80 µs.

In conclusion, we have experimentally demonstrated a scanning-probe atom interferometer operating beyond the standard quantum limit, and used it for the measurement of a microwave near-field. High-resolution measurements of microwave near-fields are relevant for the design of new microwave circuits for use in communication technology [12]. This is the first demonstration of entanglement-enhanced atom interferometry with a high spatial resolution scanning probe, and promises further high-resolution sensing and measurement applications.

References:
[1] Alexander D. Cronin, Jörg Schmiedmayer, David E. Pritchard, "Optics and interferometry with atoms and molecules", Review of Modern Physics, 81, 1051 (2009). Abstract.
[2] J. Kitching, S. Knappe, and E.A. Donley, "Atomic Sensors – A Review", IEEE Sensors Journal, 11, 1749 (2011). Abstract.
[3] Vittorio Giovannetti, Seth Lloyd, Lorenzo Maccone, "Advances in quantum metrology", Nature Photonics, 5, 222 (2011). Abstract.
[4] Caspar F. Ockeloen, Roman Schmied, Max F. Riedel, Philipp Treutlein, "Quantum Metrology with a Scanning Probe Atom Interferometer", Physical Review Letters, 111, 143001 (2013). Abstract.
[5] Max F. Riedel, Pascal Böhi, Yun Li, Theodor W. Hänsch, Alice Sinatra, Philipp Treutlein, "Atom-chip-based generation of entanglement for quantum metrology", Nature, 464, 1170 (2010). Abstract.
[6] C. Gross, T. Zibold, E. Nicklas, J. Estève, and M.K. Oberthaler, "Nonlinear atom interferometer surpasses classical precision limit", Nature, 464, 1165 (2010). Abstract.
[7] Anne Louchet-Chauvet, Jürgen Appel, Jelmer J Renema, Daniel Oblak, Niels Kjaergaard, Eugene S Polzik, "Entanglement-assisted atomic clock beyond the projection noise limit", New Journal of Physics, 12, 065032 (2010). Abstract.
[8] Ian D. Leroux, Monika H. Schleier-Smith, and Vladan Vuletić, "Orientation-Dependent Entanglement Lifetime in a Squeezed Atomic Clock", Physical Review Letters, 104, 250801 (2010). Abstract.
[9] R. Mhaskar, S. Knappe, and J. Kitching, "A low-power, high-sensitivity micromachined optical magnetometer", Applied Physics Letters, 101, 241105 (2012). Abstract.
[10] W. Wasilewski, K. Jensen, H. Krauter, J. J. Renema, M. V. Balabas, E. S. Polzik, "Quantum Noise Limited and Entanglement-Assisted Magnetometry", Physical Review Letters, 104, 133601 (2010). Abstract.
[11] S. Steinert, F. Dolde, P. Neumann, A. Aird, B. Naydenov, G. Balasubramanian, F. Jelezko, J. Wrachtrup, "High sensitivity magnetic imaging using an array of spins in diamond", Review of Scientific Instruments, 81, 043705 (2010). Abstract.
[12] S. Sayil, D.V. Kerns, jr. and S.E. Kerns, "Comparison of contactless measurement and testing techniques to a all-silicon optical test and characterization method", IEEE Trans. Instrum. Meas. 54, 2082 (2005). Abstract.