Exploring Macroscopic Quantum Mechanics with Gravitational-wave Detectors

Haixing Miao

[Haixing Miao is the recipient of the 2010 GWIC (Gravitational Wave International Committee) Thesis Prize for his PhD thesis “Exploring Macroscopic Quantum Mechanics in Optomechanical Devices" (PDF). -- 2Physics.com]

Author: Haixing Miao

Affiliation:
Australian International Gravitational Research Centre (AIGRC), University of Western Australia, Perth, Australia;
Theoretical AstroPhysics Including Relativity (TAPIR), California Institute of Technology, Pasadena, USA.

Do macroscopic objects have wavy behaviors predicted by quantum mechanics, the same as microscopic atoms? Is there any boundary or transition between the quantum world and the classical world which we experience daily? Interestingly, advanced laser interferometer gravitational-wave (GW) detectors may give answers to these fundamental questions.

Fig. 1 LIGO detector at Livingston (left). It consists of a Michelson interferometer which uses a highpower laser to measure differential motions of input test masses (ITM) and end test masses (ETM) caused by gravitational waves.

It might seem unlikely, at least from the first sight, that a GW detector (e.g., LIGO detector [1] shown in Fig. 1) can study something quantum, given its apparent classical features: (i) using a high-power laser and kilogram-scale mirrors as test masses, (ii) having these test masses widely separated by kilometers, and (iii) operating at the room temperature. How can we probe delicate quantum mechanics with such a giant? The answer lies in the fact that, to detect weak GWs from the distant universe, the GW detector has to be extremely sensitive to the tiny displacement of the kilogram test mass, even sensitive enough to probe the quantum zero-point motion of macroscopic test masses.

2Physics articles by past winners of the GWIC Thesis Prize:
Holger J. Pletsch (2009): "Deepest All-Sky Surveys for Continuous Gravitational Waves"
Henning Vahlbruch (2008): "Squeezed Light – the first real application starts now"
Keisuke Goda (2007): "Beating the Quantum Limit in Gravitational Wave Detectors"
Yoichi Aso (2006): "Novel Low-Frequency Vibration Isolation Technique for Interferometric Gravitational Wave Detectors"
Rana Adhikari (2003-5)*: "Interferometric Detection of Gravitational Waves : 5 Needed Breakthroughs"
*Note, the gravitational wave thesis prize was started initially by LIGO as a biannual prize, limited to students of the LIGO Scientific Collaboration (LSC). The first award covered the period from 1 July 2003 to 30 June 2005. In 2006, the thesis prize was adopted by GWIC, renamed, converted to an annual prize, and opened to the broader international community.

Fig. 2 Plot showing the sensitivity of LIGO Hanford detector compared with the standard quantum limit (SQL) -- a benchmark for quantumness. This figure is adopted from Ref.[2], which reports cooling of kilogram test masses down to an effective temperature of 1.4μK (Experiment is led by Nergis Mavalvala and Thomas Corbitt from MIT).

Indeed, with state-of-the-art technology, initial LIGO detector is only a factor of 10 away from the Standard Quantum Limit (SQL) that is imposed by the Heisenberg Uncertainty Principle [3] (illustrated in Fig. 2). Currently, in the GW community, significant efforts have been put into improving the detector sensitivity by reducing the classical thermal noises that cause random jittering of test masses. The future AdvLIGO [4] and other advanced GW detectors [5] under construction are anticipated to be operating at or beyond the SQL, with their sensitivities limited by noises that have purely quantum origin. To further increase the detector sensitivity, we need to manipulate the light at the quantum level, e.g. the use of quantum squeezed light [6-7]. Advanced GW detectors can be viewed as quantum devices, regardless of their bulky appearance.

Fig. 3 Figure showing schematically the creation of quantum superposition of macroscopic test masses by coherently amplifying the momentum of a single photon with advanced GW detectors. Please refer to Ref. [10] for more details of the experimental protocol.

With a sequence of studies [8-11], it is shown that, by using appropriate protocols, advanced GW detectors allow us to prepare kilogram test masses in different quantum states, and to study their quantum dynamics. For example, by superimposing a single photon―the light quantum―onto a strong light field in the GW detector, the momentum of the photon can be coherently amplified, and can even place the macroscopic test masses into a quantum superposition, as depicted schematically in Fig. 3. The GW detector, in some sense, acts as a “quantum amplifier”, and brings the quantumness of the microscopic photon into the macroscopic world.

Besides, if we simultaneously measure the common and differential motions of test masses, we can create Einstein-Podolsky-Rosen type quantum entanglement among widely separated test masses [9]. Furthermore, we can study the dynamics of such a macroscopic quantum entanglement, which allows us to explore some interesting decoherence effects that could be unique to macroscopic objects [12].

Future advanced GW detectors can, therefore, not only detect tiny ripples in the spacetime and open up a new window into observing our universe, but also help us to gain deeper understanding of quantum behaviors of macroscopic objects, which might reveal exciting new phenomena.

References:
[1] LIGO website: ligo.caltech.edu and a recent review article by the LIGO Scientific Collaboration (LSC), “LIGO: the Laser Interferometer Gravitational-wave Observatory”, Rep. Prog. Phys. 72, 076901 (2009). Abstract.
[2] LIGO Scientific Collaboration (LSC), “Observation of a kilogram-scale oscillator near its quantum ground state”, New J. Phys. 11 073032 (2009). Abstract.
[3] V. B. Braginsky and F. Y. Khalili, "Quantum Measurement", publisher: Cambridge
University Press (1992).
[4] Advanced LIGO website: advancedligo.mit.edu
[5] Advanced VIRGO website: cascina.virgo.infn.it/advirgo ; Large-scale Cryogenic Gravitational wave Telescope (LCGT) website: gw.icrr.u-tokyo.ac.jp/lcgt/
[6] H. Vahlbruch, M. Mehmet, N. Lastzka, B. Hage, S. Chelkowski, A. Franzen, S. Gossler, K. Danzmann, and R. Schnabel, “Observation of squeezed light with 10dB quantum noise reduction”, Phys. Rev. Lett. 100, 033602 (2008). Abstract.
[7] K. Goda, O. Miyakawa, E. E. Mikhailov, S. Saraf, R. Adhikari, K. McKenzie, R. Ward, S. Vass, A. J. Weinstein, and N. Mavalvala, Nature Physics 4, 472 (2008). Abstract.
[8] Helge Müller-Ebhardt, Henning Rehbein, Chao Li, Yasushi Mino, Kentaro Somiya, Roman Schnabel, Karsten Danzmann, and Yanbei Chen, “Quantum-state preparation and macroscopic entanglement in gravitational-wave detectors”, Phys. Rev. A 80, 043802 (2009). Abstract.
[9] Helge Müller-Ebhardt, Henning Rehbein, Roman Schnabel, Karsten Danzmann, and Yanbei Chen, “Entanglement of Macroscopic Test Masses and the Standard Quantum Limit in Laser Interferometry”, Phys. Rev. Lett. 100, 013601 (2008). Abstract.
[10] Farid Ya. Khalili, Stefan Danilishin, Haixing Miao, Helge Müller-Ebhardt, Huan Yang, and Yanbei Chen, “Preparing a Mechanical Oscillator in Non- Gaussian Quantum States”, Phys. Rev. Lett. 105, 070403 (2010). Abstract.
[11] Haixing Miao, Stefan Danilishin, Helge Müller-Ebhardt, Henning Rehbein, Kentaro Somiya, and Yanbei Chen, “Probing macroscopic quantum states with a sub-Heisenberg accuracy”, Phys. Rev. A 81, 012114 (2010). Abstract.
[12] Lajos Diósi, “A universal master equation for the gravitational violation of the quantum mechanics”, Phys. Lett. A 120, 377 (1987). Abstract ; Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe, Publisher: Alfred A. Knopf (2005).

Giant Magneto-Optical Faraday Rotation of Terahertz Light

Andrei Pimenov (left) and Alexey Shuvaev (right) [photo courtesy: Vienna University of Technology, Austria]

In a paper published in Physical Review Letters [1], a group of scientists from the Vienna University of Technology (TU Vienna), Austria and Universität Würzburg, Germany have reported observation of a strong Faraday effect or the rotation of the polarization of light by means of a ultra thin semiconductor. This can be used to create a transistor that works with light instead of electrical current.

Light waves can oscillate in different directions – much like a string that can vibrate up and down or left and right – depending on the direction in which it is picked. This is called the polarization of light. Physicists at the Vienna University of Technology have now, together with researchers at Würzburg University, developed a method to control and manipulate the polarization of light using ultra thin layers of semiconductor material. For future research on light and its polarization this is an important step forward – and this breakthrough could even open up possibilities for completely new computer technology. The experiment can be viewed as the optical version of an electronic transistor.

Controlling light with magnetic fields

The polarization of light can change, when it passes through a material in a strong magnetic field. This phenomenon is known as the “Faraday effect”.

The magnetic field in the thin layer rotates the light waves.

“So far, however, this effect had only been observed in materials in which it was very weak”, professor Andrei Pimenov explains. He carried out the experiments at the Institute for Solid State Physics of the TU Vienna, together with his assistant Alexey Shuvaev. Using light of the right wavelength and extremely clean semiconductors, scientists in Vienna and Würzburg could achieve a Faraday effect which is orders of magnitude stronger than ever measured before. Now light waves can be rotated into arbitrary directions – the direction of the polarization can be tuned with an external magnetic field. Surprisingly, an ultra-thin layer of less than a thousandth of a millimeter is enough to achieve this.

“Such thin layers made of other materials could only change the direction of polarization by a fraction of one degree”, says Pimenov. If the beam of light is then sent through a polarization filter, which only allows light of a particular direction of polarization to pass, the scientists can, rotating the direction appropriately, decide whether the beam should pass or not.

The key to this astonishing effect lies in the behavior of the electrons in the semiconductor. The beam of light oscillates the electrons, and the magnetic field deflects their vibrating motion. This complicated motion of the electrons in turn affects the beam of light and changes its direction of polarization.

An optical transistor

In the experiment, a layer of the semiconductor mercury telluride (HgTe) was irradiated with light in the infrared spectral range. “The light has a frequency in the terahertz domain – those are the frequencies, future generations of computers may operate with”, Pimenov believes. “For years, the clock rates of computers have not really increased, because a domain has been reached, in which material properties just don’t play along anymore.” A possible solution is to complement electronic circuits with optical elements. In a transistor, the basic element of electronics, an electric current is controlled by an external signal. In the experiment at TU Vienna, a beam of light is controlled by an external magnetic field. The two systems are very much alike. “We could call our system a light-transistor”, Pimenov suggests.

Before optical circuits for computers can be considered, the newly discovered effect will prove useful as a tool for further research. In optics labs, it will play an important role in research on new materials and the physics of light.

Reference:
[1] A. M. Shuvaev, G. V. Astakhov, A. Pimenov, C. Brüne, H. Buhmann, and L. W. Molenkamp, "Giant Magneto-Optical Faraday Effect in HgTe Thin Films in the Terahertz Spectral Range", Phys. Rev. Lett. 106, 107404 (2011). Abstract.

Interaction-based Quantum Metrology Showing Scaling Beyond the Heisenberg Limit

Mario Napolitano (left) and Morgan W. Mitchell (right)














Authors: Mario Napolitano and Morgan W. Mitchell

Affiliation: ICFO – Institute of Photonic Sciences, 08860 Castelldefels - Barcelona, Spain

The most precise modern measurement techniques are based on related interferometric techniques: whether the application is defining time-standards, measuring accelerations, magnetic fields, or even detecting the space-time distortion caused by gravitational-waves. All interferometers use the quantum superposition principle and wave-particle duality [1]: the probes, photons or atoms depending on the case, follow simultaneously two different evolutions, and these experience a phase difference due to the quantity being measured. When the paths are recombined, the flux of particles is measured, giving the result of the measurement.

The precision of such interferometers improves by using more probing particles provided that technical sources of noise are suppressed. The square-root law in Poisson statistics of random counts fixes the scale of this improvement saying that the sensitivity, namely the minimum phase difference measurable at a certain level of noise, get better as 1/√N, where N is the total number of probing particles in use. Usually, the scientific community refers to this scaling law for the sensitivity as the Standard Quantum Limit (SQL), or Shot-Noise limit.

The quest for ever-more precise measurements has motivated much of the latest research in atomic physics and quantum optics [2]. For example, most of the achievements regarding entanglement or squeezing find a natural framework in the context of quantum metrology. When applied to interferometry, entanglement means that the inherent fluctuations of each probing particle are correlated with those of another particle: in this way, the intrinsic noise of the probing system as a whole is squeezed, removing uncertainty from critical degrees of freedom and putting it into less-critical ones. In this way, the sensitivity can surpass the 1/√N standard quantum limit. In the ideal case of perfect entanglement, a NooN state, the sensitivity scales as 1/N, a law that in the community is known as the 'Heisenberg limit' [3].

Is this the best that can be done? Are there other ways to use better the probing resources? Does the Heisenberg limit apply always? Only a few years ago, theoretical studies discovered that entanglement is not the only resource that can improve measurement precision in the face of quantum noise [4,5]. According to those works, also the dynamics of the measurement process plays a very important role to establish the best achievable precision. For example, nonlinear dynamics, that is to say interaction between the probing particles, can make a difference and extend, in principle, the limit in the sensitivity.

As presented in a recent letter published in Nature [6], we were able to create the appropriate nonlinear dynamics in a polarization-based interferometer where photons are used to probe the magnetization of an ensemble of cold atoms. We investigated the sensitivity of such measurement as function of the number of photons used to probe, looking for a scaling law beyond the Heisenberg limit. In a particular regime of light intensity and detuning, we detected a polarization rotation of the probing photons due to the atomic magnetization, dependent of the photon number itself. Both this nonlinearity, and the high quality of the light-atom coupling we developed, contributed in amplifying the signal from the atoms, keeping at the same time the noise at the level of the light shot noise.

The sensitivity to the magnetization, in the nonlinear probing, was in fact scaling better than the Heisenberg limit as the photon number was increased, over a range of two orders of magnitude, Fig 1. In fact, the measured scaling was very close to the expected 1/N^3/2 for two-particle interaction [7]. With more than 20 million photons, however, incoherent processes such as optical pumping damaged to the atomic preparation and the measurement no longer improved.

Fig.1 (click on the image to see higher resolution version) : Sensitivity of the nonlinear probe versus number of interacting photons. Blue circles indicate the measured sensitivity, curves show results of numerical modeling, and the black lines indicate SQL, HL, and SH scaling for reference. Scaling surpassing the Heisenberg limit is observed over two orders of magnitude. The measured damage to the magnetization, shown as green diamonds, confirms the non-destructive nature of the measurement. Error bars for standard errors would be smaller than the symbols and are not shown.

With this experiment we opened the possibility of investigating experimentally nonlinear dynamics and interaction between quantum probes as new fundamental resources in the quest for greater sensitivity in quantum-interference-based measurements. We think that similar interaction-based measurement will soon start to be extended and tested with other techniques [8,9] although, as also we noticed in our experiment, the range of applicability will depend on the specific implementation.

Description of the experiment:

In our lab, we work with a sample of about one million of cold 87Rb atoms, held in a single-beam optical dipole trap. Pulses of polarized laser light propagate through the sample along the trap axis experiencing a very high coupling with the atomic ensemble, Fig 2a. Previous experiments demonstrated an on-resonance optical depth of above 50, which gives the figure of merit of such good coupling [10]. When instead the light is tuned off-resonant, it can probe in a dispersive, non-destructive way the angular momentum of the atomic ensemble. In particular, the polarization experiences a paramagnetic Faraday rotation proportional to the spin component along the light propagation axis.

Fig.2a (click on the image to see higher resolution version): Experimental schematic: an ensemble of 87Rb atoms,held in an optical dipole trap, is polarized by optical pumping (OP). Linear (P_1), nonlinear (P_{NL}), and a second linear (P_2) Faraday rotation probe pulses measure the atomic magnetization, detected by a shot-noise-limited polarimeter (PM). The atom number is measured by quantitative absorption imaging (AI). Fig.2b : Spectral positions of the pumping, probing, and imaging light on the D2 transition.

A key point in our experiment was the ability to calibrate the newly developed, nonlinear-probing technique against a well established and tested linear one, Fig 3. Actually, our light-atom interface is very versatile and different regimes of interaction can be addressed: in particular we could easy switch between a linear and a nonlinear interaction case. After the trap loading and an initial atomic state preparation via optical pumping with on-resonance, circular-polarized light, we probed the polarized sample under both in a linear regimes and in a nonlinear one.

Fig.3 (click on the image to see higher resolution version): 3a) Ratio of nonlinear rotation, φ_NL, to linear rotation, φ_L, vs. nonlinear probe photon number, N_NL. The data points and error bars indicate best fit and standard errors from a linear regression for a given N_NL. The red curve is a fit showing the expected nonlinear behavior, with some saturation for large N_NL. 3b)&c) φ_L, φ_NL correlation plots for two values of N_NL. The atom number N_A is varied to produce a range of φ_L and φ_NL. Green squares: no atoms N_A = 0, red circles: 1.5 x 10⁵ < N_A < 3.5 x 10⁵, blue triangles N_A ‚ 7 x 10⁵. The blue triangles are shown as a check on detector saturation, and are not included in the analysis.

In previous experiments, we demonstrated projection noise sensitivity in the linear regime, namely when low intensity and large (GHz) detuning from the resonances are used. Conversely, in this experiment we also operated in a regime of probing designed specifically to show clearly atom-mediated photon-photon interactions. We expected to excite nonlinearities like fast electronic nonlinearities, namely saturation effects in the photon absorption and stimulated emission. We used intense pulses of about 50ns, a time scale short compared with relaxation process, like optical pumping by spontaneous emission, but still long enough to define the frequency of the light within few tens of MHz. At a particular detuning, due to the symmetry of the electronic structure in alkali atoms, all the linear responses from the different atomic transitions compensate, hence only the nonlinear contributions remain, Fig 2b. Moreover, we carefully checked and excluded any possible other source of nonlinearity apart from the atoms, for example, we showed that the photodetectors continue to be linear even for the largest photon numbers.

References:
[1] Giovannetti, V., Lloyd, S. & Maccone, L. "Quantum metrology". Phys. Rev. Lett. 96, 010401 (2006). Abstract.
[2] Lee, H., Kok, P. & Dowling, J. P. "A quantum Rosetta stone for interferometry". J. Mod. Opt. 49, 2325-2338 (2002). Abstract.
[3] Holland, M. J., & Burnett, K. "Interferometric detection of optical phase shifts at the Heisenberg limit". Phys. Rev. Lett. 71, 1355 (1993). Abstract.
[4] Boixo, S., Flammia, S. T., Caves, C. M. & Geremia, J. "Generalized limits for single-parameter quantum estimation". Phys. Rev. Lett. 98, 090401(2007). Abstract.
[5] Sergio Boixo, Animesh Datta, Matthew J. Davis, Steven T. Flammia, Anil Shaji, and Carlton M. Caves, "Quantum metrology: Dynamics versus entanglement". Phys. Rev. Lett. 101, 040403 (2008). Abstract.
[6] M. Napolitano, M. Koschorreck, B. Dubost, N. Behbood, R. J. Sewell & M. W. Mitchell, "Interaction-based quantum metrology showing scaling beyond the Heisenberg limit". Nature 471, 486–489 (2011). Abstract.
[7] Napolitano, M. & Mitchell, M. W. "Nonlinear metrology with a quantum interface". New J. Phys. 12, 093016 (2010). Abstract.
[8] Woolley, M. J., Milburn, G. J. & Caves, C. M. "Nonlinear quantum metrology using coupled nanomechanical resonators". New J. Phys. 10, 125018(2008). Abstract.
[9] Choi, S. & Sundaram, B. "Bose-Einstein condensate as a nonlinear Ramsey interferometer operating beyond the Heisenberg limit". Phys. Rev. A 77, 053613 (2008). Abstract.
[10] Koschorreck, M., Napolitano, M., Dubost, B. & Mitchell, M. W. "Sub-projection-noise sensitivity in broadband atomic magnetometry". Phys. Rev. Lett. 104, 093602 (2010). Abstract.

Time-reversed Lasing and Coherent Control of Absorption

The Yale Team: Top (from L to R) A. Douglas Stone, Yidong Chong and Hui Cao; Bottom (from L to R) Heeso Noh, Li Ge, Wenjie Wan

Authors: A. Douglas Stone, Yidong Chong and Hui Cao

Affiliation: Dept. of Applied Physics, Yale University, USA

The continued development of micro and nano-fabricated lasers in recent years has led to a re-examination of the fundamental electromagnetic theory underlying laser emission. In particular, lasers based on cavities with chaotic [1] or random [2] ray dynamics have challenged physicists to understand the necessary and sufficient conditions for lasing. A formulation of laser theory has been developed (called Steady-State Ab-initio Laser Theory or SALT [3]) which treats lasing as a self-organized scattering process, wherein a zero-amplitude (or infinitesimal) input is “scattered” into a non-zero output consisting of one or more electromagnetic field modes. This new approach not only improved our understanding of modern micro and nano-fabricated lasers (including effects such as non-linear interactions within lasing modes), but also drew attention to a symmetry property of the laser equations which had been essentially unnoticed for fifty years. The symmetry is the following:

For every laser at threshold (where it is just beginning to emit coherent radiation), there exists a related optical device, termed a “coherent perfect absorber” (CPA), which will absorb completely the exact electromagnetic mode that the corresponding laser emits.

This exact relationship between electromagnetic systems can be called the “CPA theorem”. Last July, our team at Yale developed the basic theory of CPAs and proposed methods for demonstrating the effect in semiconductor cavities [4]; very recently we have achieved the first experimental demonstration of coherent control of absorption in a two-channel CPA using a simple silicon slab cavity [5], as described below.

Every laser has a gain medium – an atomic, molecular or solid substrate that is pumped with an incoherent energy source to cause it to amplify light; this amplification is characterized by a gain coefficient or (equivalently) a complex-valued index of refraction with a negative imaginary part. The corresponding CPA is obtained by replacing the gain medium of the laser by a “loss medium” which has exactly the same magnitude of absorption coefficient (imaginary index), but with opposite (positive) sign. Since the appropriate loss materials in their ground states are absorbing, no pump energy is needed in the operation of a CPA, just a tunable loss medium and a cavity which can be tailored to the required index of refraction.

The time-reversal symmetry of the laser equations at threshold then implies that absorption of the appropriate incoming (time-reversed) lasing mode at the lasing frequency will be complete. This narrow-band perfect absorption is achieved by, in effect, creating a perfect “interference trap” for this incident mode (only). This is, of course, impossible to do with a lossless cavity; energy conservation demands that the light must escape in some direction. But the CPA Theorem says it is possible to do this in an absorbing cavity at a discrete set of frequencies, if the absorption coefficient of the cavity is sufficiently tunable.

There are two key points that make coherent perfect absorbers interesting and novel. First, the perfect absorption comes from the trapping of radiation for infinite time, not by enhancing the rate at which the loss medium absorbs. Thus materials with quite low absorption coefficients at a certain wavelength can be made to absorb perfectly at those wavelengths with an appropriate cavity. Moreover, if you further increase the absorption coefficient in such a system, it absorbs less total radiation, because the trap becomes leaky. Second, and even more importantly, the CPA is, in general, a device in which the degree of absorption can be controlled optically, by varying the properties of the input fields at a given wavelength.

The reason that this is possible is that perfect absorption relies on a particular interference pattern being generated in the CPA cavity, which traps radiation indefinitely. If the corresponding laser would emit N distinct beams, then the CPA will only perfectly absorb a pattern of radiation involving all N beams illuminating the cavity with precise amplitude and phase relationships. If the N beams illuminate the cavity with a different radiation pattern, even if the frequency is correct, the radiation can be scattered out with very little absorption.

In our initial paper on CPAs we showed in a numerical simulation that a Si-SiO2 periodic cavity could be switched between 100% and 1% absorption just by varying the relative phase of the incident fields. Another important finding was that silicon is a very favorable material for the loss medium in a CPA. Because of its indirect bandgap, (which makes it a poor gain medium for a laser) there is a smooth variation of the absorption coefficient near the band edge which allows one to come very close to the ideal CPA absorption condition simply by tuning the frequency. As shown in Fig. 1, the theory said that in this manner one could pass within ten parts in a million of complete absorption (for perfectly monochromatic input beams).

Fig. 1: Semi-log plot of normalized output intensities against input wavelength, computed for a 100-micron Si slab. The blue and red curves correspond to parity-even and parity-odd scattered modes, respectively. CPAs (or near-CPAs) occur when either curve dips towards negative infinity (zero scattering).

While the theory implied that extremely complicated cavities should be capable of functioning as CPAs, we immediately decided to focus on demonstrating the effect in the simplest geometry that allowed optical control of the absorption. We had learned that the very simplest possible CPA had already been demonstrated in several forms without using the relationship to lasing [6-8]. In the earlier devices the CPA had only a single input beam, which was made to interfere with itself, either by bouncing off mirrors or by coupling in and out of an adjacent cavity. These devices showed that CPAs have potential applicability as optical modulators, detectors and filters, but because they only involved one input beam they did not exhibit optical control of absorption through variation of the phase and amplitude of the input field. Thus we set out to demonstrate this effect using a two-beam set-up, illuminating a silicon wafer acting as a low-Q Fabry-Perot cavity (“etalon”).

Fig. 2: Experimental set-up. Inset: scattered intensity (total, and to the left and sides of the wafer) when the input is tuned to a parity-odd CPA resonance frequency, showing almost complete material absorption when the input beams are out of phase.

The experimental configuration is shown in Fig. 2. A laser beam from a tunable (800 to 1050 nm) continuous-wave Ti:sapphire laser is split into two beams and routed through different arms of an interferometer onto opposite sides of a silicon wafer of thickness ~110 mm. The wavelength of the light is varied near 1000 nm at which the wafer is predicted to exhibit strong CPA resonances. At each frequency the relative phase of the two beams is varied by 180 degrees and the amount of scattered light is measured. At certain frequencies the scattered intensity varied by two orders of magnitude in response to this phase variation; these were the frequencies approaching the CPA resonance. Thus by simply varying the relative phase of our input fields at fixed frequency we controlled the absorption of the silicon wafer, changing it from very strongly absorbing to weakly absorbing. At other frequencies, between the CPA resonances, the theory predicted much smaller or even vanishing sensitivity of the absorption to the relative phase of the input beam; the experiment also confirmed this effect.

Having demonstrated the CPA effect in its general form, we hope that a number of applications for CPAs will develop. Its modulation and detection capabilities make it a candidate for use in integrated optical circuits; however one of the most useful forms of CPA, the critically-coupled fiber-ring-cavity system, has been known for quite some time [8] and is already used extensively in prototype systems. It remains to be seen if other, newer variants on the CPA inspired by our work, will be useful in this context. The CPA concept is a natural one for coherent spectroscopy of molecules in which a small coherent diagnostic signal is buried in larger incoherent noise at the same wavelength. A particularly exciting and novel potential application of the CPA concept is to strongly scattering media, which look opaque because typical radiation patterns are backscattered with very high probability. If an appropriate absorbing medium is buried below the surface of this opaque medium, the theory implies that a precisely shaped coherent signal can be made to penetrate the opaque surface layer and will be absorbed fully deep within the medium. Such a technique may find important applications in radiology and fluorescent spectroscopy.

The CPA concept is not well-suited to applications in energy harvesting and stealth technology as it is intrinsically a narrow band effect coherent effect which does not increase average absorption of broad-band incoherent radiation.

References
[1] H.E. Türeci, H. G. L. Schwefel, P. Jacquod, and A.D. Stone, “Modes of wave-chaotic dielectric resonators”, Progress in Optics, Vol 47: 75-137 (2005). Abstract.
[2] H. Cao, “Lasing in Disordered Media”, in “Progress in Optics”, ed. E. Wolf, North-Holland, vol. 45: 317-370 (2003). Abstract.
[3] H.E. Türeci, L. Ge, S. Rotter, and A. D. Stone, “Strong Interactions in Multimode Random Lasers”, Science 320, 643 (2008). Abstract.
[4] Y. D. Chong, L. Ge, H. Cao, and A.D. Stone, “Coherent Perfect Absorbers: Time-reversed Lasers”, Phys. Rev. Lett. 105, 053901 (2010). Abstract.
[5] W. Wan, Y.D. Chong, L. Ge, H. Noh, A.D. Stone, and H. Cao, “Time-Reversed Lasing and Interferometric Control of Absorption”, Science 331, 889 (2011). Abstract.
[6] R. H. Yan, R. J. Simes, L. A. Coldren, IEEE Photon. Technol. Lett. 1, 273 (1989). Abstract.
[7] M. S. Ünlü, K. Kishino, H. J. Liaw, H. Morkoç, J. Appl. Phys. 71, 4049 (1992). Abstract.
[8] A. Yariv, “Critical coupling and its control in optical waveguide-ring resonator systems”, IEEE Phot. Tech. Lett. 14, 483 (2002). Abstract.