Session T2: Non-equilibrium and Cooperativity in Cold Atoms

Open System Quantum Simulations with Cold Atoms, Molecules and Ions

We discuss concepts and possible implementations of open system quantum simulation with quantum optical systems of cold atoms, molecules and ions. We first explain the general concepts of coherent control in open quantum systems, and we relate these ideas to quantum information and non-equilibirium condensed matter physics. The specific systems to be discussed include cold atoms in optical lattices coupled coupled to a BEC as a phonon reservoir, and an open system Rydberg quantum simulator. We finally discuss theory as well as recent experiments with trapped ions which have demonstrated the basic elements of a such an open system quantum simulator.   

Number squeezed matter waves

Matter wave optics with ultracold samples has reached the point where non-classical states can be prepared and their fascinating properties can be explored. In optics, parametric down conversion is routinely used to generate light with squeezed observables as well as highly entangled photon pairs. The applications of these non-classical states range from fundamental tests of quantum mechanics to improved interferometers and quantum computation. Therefore, it is of great interest to realize such non-classical states with matter waves. Bose-Einstein condensates with non-zero spin can provide a mechanism analogous to parametric down conversion, thus enabling the generation of non-classical matter waves. We observed magnetic field dependent spin resonances, where vacuum fluctuations are amplified to macroscopic clouds. The process acts as a two-mode parametric amplifier and generates two clouds with opposite spin orientation consisting of the same number of atoms. At a total of $\sim $10000 atoms, we observe a squeezing of the number difference of -6 dB below shot noise, including all noise sources. In the future, these nonclassical matter waves can be used as a source for Bell pairs of neutral atoms as well as an input for Heisenberg limited atom interferometers.   

Mean-field transition and fluctuation phenomena in a modulated cold atom system

Periodic modulation of a magneto-optical trap can lead to parametric resonance with excitation of atomic vibrations at half the modulation frequency. For a small number of trapped atoms such resonance was seen earlier as the onset of counterphase vibrations of two atomic clouds, which were equally populated [1]. Later it was observed that, as the number of trapped atoms increases, the populations of the clouds become different [2]. This indicates spontaneous breaking of the symmetry with respect to time translation by the modulation period: it takes two periods for the system to go back to its state. We show that the effect is an ideal mean-field transition [3], with the order parameter proportional to the population difference. We describe the observations of the dependence of the order parameter on the control parameters, including nonanalytic field dependence at the critical point. We also describe anomalous behavior of the population variance. A microscopic theory of the symmetry breaking transition is developed. The transition is explained as resulting from the interplay of the long-range interatomic interaction and nonequilibrium fluctuations in the strongly modulated system. The mechanism is the modulation by the interaction, and ultimately by the cloud populations, of the effective barrier [4] that atoms have to overcome in order to switch between the clouds. The theory fully describes the observations. \\[4pt] [1] K. Kim, H. R. Noh, Y. H. Yeon, and W. Jhe, Phys. Rev. A {\bf 68}, 031403 (2003)\\[0pt] [2] K Kim et al., Phys. Rev. Lett. {\bf 96}, 150601 (2006)\\[0pt] [3] M. S. Heo et al., Phys. Rev. E {\bf 82}, 031134 (2010)\\[0pt] [4] H. B. Chan, M. I. Dykman, and C. Stambaugh, Phys. Rev. Lett. {\bf 100}, 130602 (2008)   

Emergent co-crystallization of atoms and light in multimode cavities

The self-organization of a Bose-Einstein condensate in a transversely pumped optical cavity is a process akin to crystallization: when pumped by a laser of sufficient intensity, the coupled matter and light fields evolve, spontaneously, into a spatially modulated pattern (i.e., crystal). In cavities having multiple degenerate modes, the quasi-continuum of possible crystalline arrangements, and the continuous symmetry breaking associated with the adoption of a particular one, give rise to phenomena such as phonons, defects, and frustration. A nonequilibrium field-theoretic approach enables the exploration of the self-organization of a Bose-Einstein condensate in a pumped, lossy optical cavity. At nonzero temperatures, this organization occurs via a fluctuation-driven first-order phase transition of the Brazovskii class; the transition persists to zero temperature and crosses over into a quantum phase transition. The field- theoretic approach also enables the investigation of the role of nonequilibrium fluctuations in the self-organization transition, as well as the nucleation of ordered-phase droplets, the nature and energetics of topological defects, supersolidity in the ordered phase, and the possibility of frustration effects controlled by the cavity geometry. \hfil\break\noindent Work done in collaboration with Sarang Gopalakrishnan and Benjamin L.~Lev.