D. Nagy

Dicke-model phase transition in the quantum motion of a Bose-Einstein condensate in an optical cavity.

We show that the motion of a laser-driven Bose-Einstein condensate in a high-finesse optical cavity realizes the spin-boson Dicke model. The quantum phase transition of the Dicke model from the normal to the superradiant phase corresponds to the self-organization of atoms from the homogeneous into a periodically patterned distribution above a critical driving strength. The fragility of the ground state due to photon measurement induced backaction is calculated.

Self-organization of a Bose-Einstein condensate in an optical cavity

Abstract.The spatial self-organization of a Bose-Einstein condensate (BEC) in a high-finesse linear optical cavity is discussed. The condensate atoms are laser-driven from the side and scatter photons into the cavity. Above a critical pump intensity the homogeneous condensate evolves into a stable pattern bound by the cavity field. The transition point is determined analytically from a mean-field theory. We calculate the lowest lying Bogoliubov excitations of the coupled BEC-cavity system and the quantum depletion due to the atom-field coupling.

Critical exponent of a quantum-noise-driven phase transition: The open-system Dicke model

The quantum phase transition of the Dicke model has been observed recently in a system formed by motional excitations of a laser-driven Bose-Einstein condensate coupled to an optical cavity [Baumann et al., Nature (London) 464, 1301 (2010)]. The cavity-based system is intrinsically open: photons leak out of the cavity where they are detected. Even at zero temperature, the continuous weak measurement of the photon number leads to an irreversible dynamics toward a steady state. In the framework of a generalized Bogoliubov theory, we show that the steady state exhibits a dynamical quantum phase transition. We find that the critical point and the mean field are only slightly modified with respect to the phase transition in the ground state. However, the critical exponents of the singular quantum correlations are significantly different in the two cases. There is also a drastic modification of the atom-field entanglement, since the divergence of the logarithmic negativity of the ground state at the critical point is suppressed and a finite entanglement is found in the steady state.

Quantum noise of a Bose-Einstein condensate in an optical cavity, correlations, and entanglement

A Bose-Einstein condensate of ultracold atoms inside the field of a laser-driven optical cavity exhibits dispersive optical bistability. We describe this system by using mean-field approximation and by analyzing the correlation functions of the linearized quantum fluctuations around the mean-field solution. The entanglement and the statistics of the atom-field quadratures are given in the stationary state. It is shown that the mean-field solution, that is, the Bose-Einstein condensate, is robust against entanglement generation for most of the phase diagram.

Excess Noise Depletion of a Bose-Einstein Condensate in an Optical Cavity

Quantum fluctuations of a cavity field coupled into the motion of ultracold bosons can be strongly amplified by a mechanism analogous to the Petermann excess noise factor in lasers with unstable cavities. For a Bose-Einstein condensate in a stable optical resonator, the excess noise effect amounts to a significant depletion on long time scales.

Photonic tuning of Beliaev damping in a superfluid

We show that the damping rate of elementary excitations of hybrid systems close to a phase transition can undergo a remarkable resonance like enhancement before mode softening takes place. In particular, we consider the friction of a collective density wave in a homogeneous superfluid of weakly interacting bosonic atoms coupled to the electromagnetic field of a single mode optical resonator. Here the Beliaev damping can thus be controlled by an external laser drive and be enhanced by several orders of magnitude.

Collective cooling of atoms in a ring cavity

We study the cooling effect induced by a transversely pumped ring cavity on the motion of N linearly polarizable particles, all of which are trapped in the same cavity. We derive the friction tensor including cross friction terms and compare it to the friction coefficient of single-atom cavity cooling. We find that atoms that are not trapped by the cavity field are cooled independently with the same efficiency as a single untrapped atom. For atoms self-trapped in the cavity field, however, collective effects kick in. These result in an N-fold increase of the friction on the center-of-mass mode, however, all other modes of motion are practically not cooled by the cavity. This shows that cavity cooling works efficiently for many particles cooled collectively, and allows us to reach the regime where the particles are deeply trapped in harmonic wells. There it has to be complemented by other cooling methods, e.g. sideband cooling.

Cavity optomechanics with a trapped, interacting Bose-Einstein condensate

The dispersive interaction of a Bose-Einstein condensate with a single mode of a high-finesse optical cavity realizes the radiation pressure coupling Hamiltonian. In this system the role of the mechanical oscillator is played by a single condensate excitation mode that is selected by the cavity mode function. We study the effect of atomic s-wave collisions and show that it merely renormalizes parameters of the usual optomechanical interaction. Moreover, we show that even in the case of strong harmonic confinement – which invalidates the use of Bloch states – a single excitation mode of the Bose-Einstein condensate couples significantly to the light field, that is the simplified picture of a single “mechanical” oscillator mode remains valid.

Dipole-dipole instability of atom clouds in a far-detuned optical dipole trap

The effect of the dipole-dipole interaction on the far-off-resonance optical dipole trapping scheme is calculated by a mean-field approach. The trapping laser field polarizes the atoms and the accompanying dipole-dipole energy shift deepens the attractive potential minimum in a pancake-shaped cloud. At high density the thermal motion cannot stabilize the gas against self-contraction and an instability occurs. We calculate the boundary of the stable and unstable equilibrium regions on a two-dimensional phase diagram of the atom number and the ratio of the trap depth to the temperature. We discuss the limitations imposed by the dipole-dipole instability on the parameters needed to reach Bose-Einstein condensation in an optical dipole trap.