Ultralong Lasers Cavity Length Limits Explored

Juan Diego Ania-Castañón of Instituto de Óptica (CSIC), Spain

[This is an invited article based on a recent work by the author and his collaborators from UK and Russia. -- 2Physics.com]

Author: Juan Diego Ania Castañón
Affiliation: Instituto de Óptica, CSIC, Spain

Since their inception, lasers have been considered simply as sources of light. However, ultralong lasers implemented in optical fiber can also be seen as unique transmission media opening the way to a new outlook on information transmission and secure communications.

In our recent paper in Physical Review Letters [1] we present a study of the physical mechanisms that restrict the achievable cavity length in a fiber laser cavity, achieving in the process what is to date the longest laser ever built, reaching 270 km.

P. Harper, S. Turitsyn, D. Churkin, A.E. El-Taher (Photonics Research Group, Aston University, UK)

Ultralong lasers, first proposed in 2004 [2] and experimentally demonstrated in 2006 [3], have been shown to induce virtual transparency in optical fiber, offering quasi-lossless transmission conditions which are ideal for the implementation of soliton-based systems and signal processing. Departing from previous application-oriented studies, we set out on this occasion to explore the fundamental limits of laser operation. This endeavor has resulted in the discovery of interesting new physical regimes of operation, different from those observed in traditional lasers.

S. Kablukov, E.V. Podivilov and S. Babin (Institute of Automation of Electrometry, Russia)

A typical ultra-long Raman fiber laser consists of one or more reels of optical fiber, which act as both the active medium and the potential transmission medium, one or more pump sources that inject radiation into the cavity in order to induce lasing, and a set of fiber Bragg grating reflectors (tuned to the Stokes wavelength) which delimit the cavity. These pump sources are themselves usually standard short-length Raman fiber lasers. The Raman frequency shift in optical fiber is of ~ 13 THz, which translates into roughly 100 nm at the usual infrared wavelengths used for telecommunication.

Taking advantage of the reduced attenuation offered by standard optical fiber in the telecommunication spectral window, we were able to strech cavity length up to 270 km while still retaining a resolvable cavity mode structure, confirming the formation of an ultralong standing electromagnetic wave. Our initial pump sources at 1450 nm were used to induce lasing in the cavity at the corresponding Stokes wavelength of 1550 nm.

Of course, such an enormous resonant cavity presents a similarly extraordinary number of longitudinal cavity modes [4]. Indeed, the observed spectral separation between modes clearly follows the classical formula ∆ν =c/2nL, where n is the refractive index of the fiber core, c the speed of light and L the cavity length, which for a typical grating bandwidth of 100 GHz, brings the number of modes to the hundreds of millions. These modes are broadened and eventually washed out as they interact with each other through intensity-dependent, turbulent-like four-wave mixing processes in the fibre, meaning that in order for the mode-structure to be resolvable at such extended cavity lengths, Stokes wave intensity must be kept low.

Perhaps even more interestingly, at such long cavity lengths there is an additional physical effect that contributes to the washing out of the cavity modes: Rayleigh backscattering. The random backreflection of Stokes photons by Silica molecules along the optical fiber forms a family of overlapping cavities of randomly varying length. Our calculations show that for a system such as ours, the amount of radiation reflected in these random scatterings and the amount of radiation reflected at the ultra-long laser cavity gratings themselves become comparable when the length of fiber is of the order of 250 km, in agreement with the observed experimental limit for mode resolution.

Ultralong lasers already present unique applications in a variety of areas ranging from the implementation of effectively lossless broadband transmission links, the posibility of new classical means for secure key distribution and the design of highly efficient supercontinuum sources, but most importantly, they represent a new and rich field of study that combines diverse areas of Physics such as nonlinear science, the theory of disordered systems or wave turbulence. This richness allows us to anticipate that new applications and technologies of ultralong lasers will continue to emerge in the future.

References
[1] S.K. Turitsyn, J.D. Ania-Castañón, S.A. Babin, V. Karalekas, P. Harper, D. Churkin, S.I. Kablukov, A.E. El-Taher, E. V. Podivilov, and V. K. Mezentsev, “270 km Ultralong Raman Fiber Laser”, Phys. Rev. Lett. 103 133901 (2009). Abstract.
[2] J.D. Ania-Castañón, “Quasi-lossless transmission using second-order Raman amplification and fibre Bragg gratings”, Optics Express, 12(19), 4372-4377 (2004). Abstract.
[3] Juan Diego Ania-Castañón, Tim J. Ellingham, R. Ibbotson, X. Chen, L. Zhang, and Sergei K. Turitsyn, “Ultralong Raman Fiber Lasers as Virtually Lossless Optical Media”, Phys. Rev. Lett. 96 23902 (2006). Abstract.
[4] S. A. Babin, V. Karalekas, P. Harper, E. V. Podivilov, V. K. Mezentsev, J. D. Ania-Castañón, and S. K. Turitsyn, “Experimental demonstration of mode structure in ultralong Raman fiber lasers”, Opt. Lett. 32(9) 1135-1137 (2007). Abstract.

Simulating the Physics of a Free Dirac Particle

Christian Roos

[This is an invited article based on a recently published work by the author and his collaborators from Austria and Spain -- 2Physics.com]

Author: Christian Roos

Affiliation: Institut für Experimentalphysik, Universität Innsbruck, Austria
and
Institute for Quantum Optics and Quantum Information
Austrian Academy of Sciences

By the mid 1920s physicists had established the dynamics of quantum particles in the non-relativistic limit. The celebrated Schrödinger equation established a framework that allowed tackling a vast range of problems in atomic, molecular and solid state physics. However, the equation is limited to the regime of particles with velocities that are small compared to the speed of light. In 1928, Dirac put forward an equation to describe electrons in a way that successfully reconciles quantum physics with special theory of relativity. The Dirac equation provides a natural explanation of spin as an intrinsic property of the electron. It has not only positive energy solutions but also solutions with negative energies which led to the prediction of anti-matter.

In 1930, at a time when the interpretation of solutions to Dirac equation was still debated, Schrödinger noticed another peculiar feature: the equation admits solutions where the centre-of-mass of a quantum particle exhibits a trembling motion, called Zitterbewegung, in the absence of external forces [1]. This effect is surprising because according to Newton’s first law, a particle that experiences no forces should move in a straight line. In real quantum particles, such as electrons, this trembling motion would have a very small amplitude (10^-13m) and an extremely high frequency (10²¹ Hz). Moreover, it arises only as an interference effect in solutions comprised of positive and negative energy components. Such solutions, which might seem irrelevant, arise, however, in the presence of external fields. For free electrons, this phenomenon does to seem to be experimentally accessible.

It is, however, possible to engineer other quantum systems such that they mimic the physics of the Dirac equation. One such system is an ion held in an ion trap and cooled and manipulated by laser light [2]. How can such a trapped non-relativistic quantum particle simulate the physics of a free Dirac particle? To answer this question, it is helpful to look first at the case of a classical particle held in a harmonic potential. The motion of this particle is described by a circle in phase space. For a particle that is resonantly excited by an external driving force, its phase space trajectory will turn into a helix. In a frame where the phase space coordinates rotate at the resonance frequency of the particle, the helix turns into a straight line which the particle follows with constant velocity, i.e. the particle looks like a free particle in the absence of forces.

The same approach can be followed in the case of a relativistic quantum particle. Using a trapped ion, internal energy levels of the ion can be used for encoding the four spinor components representing the particle’s wave function. The term that couples the particle’s momentum operator and the spinor components in the Dirac equation can be simulated in the trapped-ion case by laser beams coupling the ion’s internal states with its motion. The term representing the ion’s rest energy is simulated by another laser-ion interaction that modifies the internal-state energies. In this way, a perfect match is achieved between the form of the Dirac equation and the Schrödinger equation describing the quantum physics of the trapped ion.

In an experiment reported in the Nature issue of the 7th January [3], this proposal is realized using a single trapped ⁴⁰Ca⁺ held in a linear ion trap (see Fig.1).

Fig.1: Experimental setup. An ion trap set up in a ultra-high vacuum system is used to store a ⁴⁰Ca⁺ ion. The ion is illuminated by laser light that serves to laser-cool, manipulate and detect the particle. (Image Credit: C. Lackner, IQOQI)

The goal of the experiment consists in observing the trembling motion predicted by Schrödinger. For this, the ion’s motion is first laser-cooled to the lowest energy state in which the ion is localized to a space of about 10 nm, the uncertainty in the position being due to the Heisenberg uncertainty relation. Then, for a certain amount of time, a suitable combination of laser beams is switched on to simulate the physics of the Dirac equation. The final step consists in a measurement that detects the change in the ion’s position. These three basic steps take no longer than 20 ms to carry out. They are repeated over and over again in order to measure the ion motion as a function of time. In perfect agreement with Schrödinger’s prediction, we indeed observe a trembling motion which is shown in Fig. 2.

Fig.2: Measured ‘Zitterbewegung’. (a) Average position of the ion as a function of time. The ion motion is composed of a uniform motion on top of which the trembling motion appears. (b) Time evolution of the ion’s wave function. Its two spinor components are shown in red and blue. The trembling motion disappears as soon as the two spinor components are no longer spatially overlapped.

Why can this experiment be called a quantum simulation? In the 1980's Richard Feynman and others proposed a new method for approaching quantum mechanical problems that are too hard to solve on ordinary computers. Their idea was to use a more accessible quantum system to simulate quantum effects of interest. To date, only a few quantum systems can be controlled well enough to act as a quantum simulator. In our experiment, we have performed a quantum simulation of a free Dirac particle using a single trapped ion manipulated with laser light. In this case, the quantum-mechanical state space has no more than 100 dimensions, a size that can be handled perfectly well by any current desktop computer. So the experiment is far from outperforming computers. But the small size of the quantum system is also an advantage because it allows us to compare experiment and theoretical prediction and in this way test the concept of a quantum simulator. The hope is that in the future systems of trapped ions or neutral atoms held in optical lattices might be used to simulate and study quantum phenomena that can no longer be analyzed by computer simulations.

References
[1] “Über die kräftefreie Bewegung in der relativistischen Quantenmechanik”, Sitz. Preuss. Akad. Wiss. Phys.-Math. Kl. 24, 418–428 (1930).
[2] “Robust Dirac equation and quantum relativistic effects in a single trapped ion”, L. Lamata, J. León, T. Schätz, E. Solano. Phys. Rev. Lett. 98, 253005 (2007). Abstract.
[3] “Quantum simulation of the Dirac equation”, R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, C. F. Roos, Nature 463, 68 (2010). Abstract.

The Mechanism behind Superinsulation

From Left to Right: Valerii Vinokur, Tatyana Baturina and Nikolai Chtchelkatchev (photo courtesy: Argonne National Laboratory)

Scientists at the U.S. Department of Energy's Argonne National Laboratory have discovered the microscopic mechanism behind the phenomenon of superinsulation, the ability of certain materials to completely block the flow of electric current at low temperatures.

The essence of the mechanism is what the authors termed "multi-stage energy relaxation" in a recent paper [1] published in Physical Review Letters. An earlier paper [2] on the discovery of superinsulation was published in Nature in April, 2008.

Traditionally, energy dissipation accompanying current flow is viewed as disadvantageous, as it transforms electricity into heat and thus results in power losses. In arrays of tunnel junctions that are the basic building units of modern electronics, this dissipation permits the generation of current.

Argonne scientist Valerii Vinokour, along with Russian scientists Nikolai Chtchelkatchev (Moscow Institute of Physics and Technology) and Tatyana Baturina (Institute of Semiconductor Physics, Novosibirsk), found that at very low temperatures the energy transfer from tunneling electrons to the thermal environment may occur in several stages.

An electron microscopy image of titanium nitride, on which the effect of superinsulation was first observed [image courtesy: Argonne National Laboratory]

“First, the passing electrons lose their energy not directly to the heat bath; they transfer their energy to electron-hole plasma, which they generate themselves,” Vinokour said. “Then this plasma 'cloud' transforms the acquired energy into the heat. Thus, tunneling current is controlled by the properties of this electron-hole cloud.”

As long as the electrons and holes in the plasma cloud are able to move freely, they can serve as a reservoir for energy—but below certain temperatures, electrons and holes become bound into pairs. This does not allow for the transfer of energy from tunneling electrons and impedes the tunneling current, sending the conductivity of the entire system to zero.

“Electron-hole plasma disappears from the game and electrons cannot generate the energy exchange necessary for tunneling,” Vinokour said. Because the current transfer in thin films and granular systems that exhibit superinsulating behavior relies on electron tunneling, the multistage relaxation explains the origin of the superinsulators.

Superinsulation is the opposite of superconductivity; instead of a material that has no resistivity, a superinsulator has a near-infinite resistance. Integration of the two materials may allow for the creation of a new class of quantum electronic devices. This discovery may one day allow researchers to create super-sensitive sensors and other electronic devices.

Reference
[1] N. M. Chtchelkatchev, V. M. Vinokur, and T. I. Baturina, "Hierarchical Energy Relaxation in Mesoscopic Tunnel Junctions: Effect of a Nonequilibrium Environment on Low-Temperature Transport", Physical Review Letters, 103, 247003 (2009). Abstract.
[2] Valerii M. Vinokur, Tatyana I. Baturina, Mikhail V. Fistul, Aleksey Yu. Mironov, Mikhail R. Baklanov and Christoph Strunk, "Superinsulator and quantum synchronization", Nature, 452, 613-615 (3 April 2008). Abstract.

[We thank Argonne National Laboratory, IL, USA for materials used in this report]

Everlasting Quantum Wave: Prediction of A New Form of Soliton in Ultracold Gases

Radha Balakrishnan [photo courtesy: Indian Academy of Sciences]

Solitary waves that run a long distance without losing their shape or dying out are a special class of waves called solitons. These everlasting waves are exotic enough, but theoreticians at the Joint Quantum Institute (JQI, a collaboration of the National Institute of Standards and Technology and the University of Maryland), and their colleagues from the Institute of Mathematical Sciences (India) and the George Mason University, now believe that there may be a new kind of soliton that’s even more special. Expected to be found in certain types of ultracold gases, the new soliton would not be just a low-temperature atomic curiosity, it also may provide profound insights into other physical systems, including the early universe.

Indubala Satija [photo courtesy: Joint Quantum Institute, NIST/U. Maryland]

Solitons can occur everywhere. In the 1830s, Scottish scientist John Scott Russell first identified them while riding along a narrow canal, where he saw a water wave maintaining its shape over long distances, instead of dying away. This “singular and beautiful” phenomenon, as Russell termed it, has since been observed, created and exploited in many systems, including light waves in optical-fiber telecommunications, the vibrational waves that sweep through atomic crystals, and even “atom waves” in Bose-Einstein condensates (BECs), an ultracold state of matter.

Atoms in BECs can join together to form single large waves that travel through the gas. The atom waves in BECs can even split up, interfere with one another, and cancel each other out. In BECs with weakly interacting atoms, this has resulted in observations of “dark solitons,” long-lasting waves that represent absences of atoms propagating through the gas, and “bright” solitons (those carrying actual matter).

Charles W. Clark [photo courtesy: Joint Quantum Institute, NIST/ U. Maryland]

By taking a new theoretical approach, the new work predicts a third, even more exotic “immortal” soliton—never before seen in any other physical system. This new soliton can occur in BECs made of “hard-core bosons”—atoms that repel each other strongly and thus interact intensely —organized in an egg-crate-like arrangement known as an “optical lattice.”

In 1990, one of the coauthors of the present work, Radha Balakrishnan of the Institute of Mathematical Sciences in India, wrote down the mathematical description of these new solitons, but considered her work merely to approximate the behavior of a BEC made of strongly interacting gas atoms. With the subsequent observations of BECs, the JQI researchers recently realized both that Balakrishnan’s equations provide an almost exact description of a BEC with strongly interacting atoms, and that this previously unknown type of soliton actually can exist. While all previously known solitons die down as their wave velocity approaches the speed of sound, this new soliton would survive, maintaining its wave height (amplitude) even at sonic speeds.

[Image credit: I. Satija et al., Joint Quantum Institute] A newly predicted “immortal” soliton (left) as compared to a conventional “dark” soliton (right). The horizontal axis depicts the width of the soliton wavefronts (bounded by yellow in the left panel and purple on the right panel, with different colors representing different wave heights). The vertical axis corresponds to the speed of the soliton as a fraction of the velocity of sound. The immortal soliton on the left maintains its shape right up to the sound barrier.

If the “immortal” soliton could be created to order, it could provide a new avenue for investigating the behavior of strongly interacting quantum systems, whose members include high-temperature superconductors and magnets. As atoms cooling into a BEC represent a phase transition (like water turning to ice), the new soliton could also serve as an important tool for better understanding phase transitions, even those that took place in the early universe as it expanded and cooled.

Reference
“Particle-hole asymmetry and brightening of solitons in a strongly repulsive Bose-Einstein condensate,”
R. Balakrishnan, I.I. Satija and C.W. Clark,
Physical Review Letters, vol. 103, p. 230403 (2009) Abstract.

[We thank National Institute of Standard and Technology for materials used in this posting]