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arXiv:quant-ph/0508172 · Physical Review Letters

Cold Atom Dynamics in a Quantum Optical Lattice Potential

Christoph Maschler, Helmut Ritsch

Published Dec 19, 2005• 189 citations
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Abstract

We study a generalized cold atom Bose-Hubbard model, where the periodic optical potential is formed by a cavity field with quantum properties. On the one hand, the common coupling of all atoms to the same mode introduces cavity-mediated long-range atom-atom interactions, and, on the other hand, atomic backaction on the field introduces atom-field entanglement. This modifies the properties of the associated quantum phase transitions and allows for new correlated atom-field states, including superposition of different atomic quantum phases. After deriving an approximative Hamiltonian including the new long-range interaction terms, we exhibit central physical phenomena at generic configurations of few atoms in few wells. We find strong modifications of population fluctuations and next-nearest-neighbor correlations near the phase transition point.

DOI
10.1103/physrevlett.95.260401

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We study a generalized cold atom Bose-Hubbard model, where the periodic optical potential is formed by a cavity field with quantum properties. On the one hand, the common coupling of all atoms to the same mode introduces cavity-mediated long-range atom-atom interactions, and, on the other hand, atomic backaction on the field introduces atom-field entanglement. This modifies the properties of the associated quantum phase transitions and allows for new correlated atom-field states, including superposition of different atomic quantum phases. After deriving an approximative Hamiltonian including the new long-range interaction terms, we exhibit central physical phenomena at generic configurations of few atoms in few wells. We find strong modifications of population fluctuations and next-nearest-neighbor correlations near the phase transition point.
This is a review of state-of-the-art theory and experiment of the motion of cold and ultracold atoms coupled to the radiation field within a high-finesse optical resonator in the dispersive regime of the atom-field interaction with small internal excitation. The optical dipole force on the atoms together with the backaction of atomic motion onto the light field gives rise to a complex nonlinear coupled dynamics. As the resonator constitutes an open driven and damped system, the dynamics is nonconservative and in general enables cooling and confining the motion of polarizable particles. In addition the emitted cavity field allows for real-time monitoring of the particle's position with minimal perturbation up to subwavelength accuracy. For many-body systems, the resonator field mediates controllable long-range atom-atom interactions, which set the stage for collective phenomena. Besides the correlated motion of distant particles, one finds critical behavior and nonequilibrium phase transitions between states of different atomic order in conjunction with superradiant light scattering. Quantum-degenerate gases inside optical resonators can be used to emulate optomechanics as well as novel quantum phases such as supersolids and spin glasses. Nonequilibrium quantum phase transitions as predicted by, e.g., the Dicke Hamiltonian can be controlled and explored in real time via monitoring the cavity field. In combination with optical lattices, the cavity field can be utilized for nondestructive probing Hubbard physics and tailoring long-range interactions for ultracold quantum systems.
Interactions between many-body atomic systems in optical lattices and light in cavities induce long-range and correlated atomic dynamics beyond the standard Bose-Hubbard model, due to the global nature of the light modes. We characterize these processes, and show that uniting such phenomena with dynamical constraints enforced by the backaction resultant from strong light measurement leads to a synergy that enables the atomic dynamics to be tailored, based on the particular optical geometry, exploiting the additional structure imparted by the quantum light field. This leads to a range of tunable effects such as long-range density-density interactions, perfectly correlated atomic tunneling, superexchange, and effective pair processes. We further show that this provides a framework for enhancing quantum simulations to include such long-range and correlated processes, including reservoir models and dynamical global gauge fields.
We determine the quantum ground-state properties of ultracold bosonic atoms interacting with the mode of a high-finesse resonator. The atoms are confined by an external optical lattice, whose period is incommensurate with the cavity mode wavelength, and are driven by a transverse laser, which is resonant with the cavity mode. While for pointlike atoms photon scattering into the cavity is suppressed, for sufficiently strong lasers quantum fluctuations can support the buildup of an intracavity field, which in turn amplifies quantum fluctuations. The dynamics is described by a Bose-Hubbard model where the coefficients due to the cavity field depend on the atomic density at all lattice sites. Quantum Monte Carlo simulations and mean-field calculations show that, for large parameter regions, cavity backaction forces the atoms into clusters with a checkerboard density distribution. Here, the ground state lacks superfluidity and possesses finite compressibility, typical of a Bose glass. This system constitutes a novel setting where quantum fluctuations give rise to effects usually associated with disorder.
Ultracold atoms in an optical lattice Bloch oscillate when subject to a constant force. In the first work presented in this thesis we have theoretically studied the scenario where the optical lattice potential is provided by the electric field inside an optical cavity. The coherent atom-light interaction in a cavity gives rise to a backaction effect on the light field which can modify the intracavity field amplitude and phase. In our first treatment of this problem we model the cavity light field and atoms by classical fields and solve the coupled atom-light equations of motion. As a result, we find that the amplitude and phase of the transmitted light field is modulated at the Bloch frequency. Remarkably, the Bloch frequency itself is not modified by the backaction. Thus the transmitted light field can be used to observe the oscillations continuously, allowing high-precision measurement with small clouds of atoms. In the second problem presented in this thesis, we explore the band structure of the steady state solutions of the atom-cavity system. A crucial first step towards determining the band structure is the identification of an energy functional that describes the coupled atom-light system. Although, we do not include direct atom-atom interactions in our models, the coupling of the atoms to the single mode light field of the cavity introduces an effective mutual interaction which is correctly taken into account by the energy functional we introduce. Corresponding to each point in the band there exists a steady state light field associated with an average cavity photon number. The dispersive nonlinear atom-light interaction can lead to bistable solutions for this intracavity photon number. For parameters where the atom-cavity system exhibits bistability, the atomic band structure develops loop structures akin to the ones predicted for Bose-Einstein condensates in ordinary (non-cavity) optical lattices. However, in our case the nonlinearity derives from the cavity backaction rather than from direct interatomic interactions. We find both bi- and tri-stable regimes associated with the lowest band, and show that the multistability we observe can be analysed in terms of swallowtail catastrophes. Dynamic and energetic stability of the meanfield solutions is also studied, and we show that the bistable solutions have, as expected, one unstable and two stable branches. The presence of loops in the band structure can lead to a breakdown in adiabaticity during Bloch oscillations as the entire band is sampled during the dynamics. We therefore use the insight gleaned from this work in choosing parameters for the Bloch oscillation measurement proposal presented in the rest of the thesis. In the third work presented in the thesis, we go beyond the mean field description and consider effects of the quantised nature of the light and atomic fields. The cavity light field is always in contact with external electromagnetic fields through the partially transmissive mirrors. This coupling to the external modes enters as quantum noise in the dynamics of the intracavity field and can also be viewed as a manifestation of quantum measurement backaction corresponding to the continuous observation of the transmitted light field. We solve the Heisenberg-Langevin equations for linearized fluctuations about the atomic and optical meanfields and examine how this influences the signal-to-noise ratio of a measurement of external forces using this system. In particular, we investigate the effects of changing the number of atoms, the intracavity lattice depth, and the atom-light coupling strength, and show how resonances between the Bloch oscillation dynamics and the quasiparticle spectrum have a strong influence on the signal-to-noise ratio as well as heating effects. One of the hurdles we overcome along the way is the proper treatment of fluctuations about time-dependent meanfields in the context of cold atom cavity-QED.
We investigate the nonlinear light-matter interaction of a Bose-Einstein condensate trapped in an external periodic potential inside an optical cavity which is weakly coupled to vacuum radiation modes and driven by a transverse pump field. Based on a generalized Bose-Hubbard model which incorporates a single cavity mode, we include the collective backaction of the atoms on the cavity light field and determine the nonequilibrium quantum phases within the nonperturbative bosonic dynamical mean-field theory. With the system parameters adapted to recent experiments, we find a quantum phase transition from a normal phase to a self-organized superfluid phase, which is related to the Hepp-Lieb-Dicke superradiance phase transition. For even stronger pumping, a self-organized Mott insulator phase arises.
Extended Bose-Hubbard models with nearest-neighbor interaction describe minimally the effect of long-range interaction on ultracold atoms in deep optical lattices. The rotation of such optical lattices subjects such neutral cold atoms to the effect of an artificial magnetic field. The modification of the phase boundaries of the density-wave and Mott-insulator phases due to this rotation are shown to be related to the edge spectrum of spinorial and scalar Harper equations. Corresponding profiles of the checkerboard vortex states with sublattice modulated superfluid order parameter near the density-wave phase boundary are calculated.