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 back action is calculated.PACS numbers: 05.30. Rt,37.30.+i,42.50.Nn A thermal cloud of cold atoms interacting with a single mode of a high-finesse optical cavity can undergo a phase transition when tuning the power of a laser field which illuminates the atoms from a direction perpendicular to the cavity axis [1,2,3,4]. Below a threshold power, the thermal fluctuations stabilize the homogeneous distribution of the cloud, and photons scattered by the atoms into the cavity destructively interfere, rendering the mean optical field to be zero. Above threshold, the atoms self-organize into a wavelength-periodic crystalline order bound by the radiation field which, in this case, is composed of the constructive interference of photons scattered off the atoms from the laser into the cavity. The same phase transition can happen for Bose-Einstein condensed ultra-cold atoms, that is exempt from thermal fluctuations. For low pump power at zero temperature, the homogeneous phase is stabilized by the kinetic energy and the atom-atom collisions, a sharp transition threshold is thus expected [5,6]. In both examples the selforganization is a non-equilibrium phase transition with the distinct phases being stationary states of the drivendamped dynamics.In this paper we show that the Hamiltonian underlying the spatial self-organization is analogous to the Dicke-type Hamiltonian [7] and the transition to the selforganized phase can thus be identified with the superradiant quantum phase transition [8]. Hence, the quantum motion of ultracold atoms in a cavity effectively realizes the Dicke model and may lead to the first experimental studies on this paradigmatic system. The accessibility of such a Hamiltonian dynamics is limited by the coupling to the environment. We explore how quantum noise infiltrates and depletes the ground state [9], imposing thereby a condition on the time duration allowed for the adiabatic variation of the macroscopically populated ground state by means of tuning an external parameter.We consider a zero-temperature Bose-Einstein condensate of a number of N atoms of mass m which is inside a high-Q optical cavity with a single quasi-resonant mode of frequency ω C . Such a system has been realized and manipulated in several recent experiments [10,11,12,13,14,15]. The atoms are coherently driven from the side by a pump laser field. The pump laser frequency ω is detuned far below the atomic resonance frequency ω A , so that the atom-pump (red) detuning ∆ A = ω − ω A far exceeds the rate of spontaneous emission. One can then adiabatically eliminate the excited atomic level and the at...

We develop a mean-field model describing the Hamiltonian interaction of ultracold atoms and the optical field in a cavity. The Bose-Einstein condensate is properly defined by means of a grandcanonical approach. The model is efficient because only the relevant excitation modes are taken into account. However, the model goes beyond the two-mode subspace necessary to describe the self-organization quantum phase transition observed recently. We calculate all the second-order correlations of the coupled atom field and radiation field hybrid bosonic system, including the entanglement between the two types of fields.

We present a general theory for calculating the damping rate of elementary density-wave excitations in a Bose-Einstein condensate strongly coupled to a single radiation field mode of an optical cavity. Thereby we give a detailed derivation of the huge resonant enhancement in the Beliaev damping of a density-wave mode, predicted recently by Kónya et al. [Phys. Rev. A 89, 051601(R) (2014)]. The given density-wave mode constitutes the polaritonlike soft mode of the self-organization phase transition. The resonant enhancement takes place, in both the normal and the ordered phases, outside the critical region. We show that the large damping rate is accompanied by a significant frequency shift of this polariton mode. Going beyond the Born-Markov approximation and determining the poles of the retarded Green's function of the polariton, we reveal a strong coupling between the polariton and a collective mode in the phonon bath formed by the other density-wave modes.

We show that the Beliaev damping of elementary excitations in a homogeneous Bose-Einstein condensate can undergo resonant enhancement by several orders of magnitude when the superfluid is interacting with a far-detuned radiation field of an optical resonator. The photonic tuning of the quasiparticle damping can be controlled by an external laser drive. DOI: 10.1103/PhysRevA.89.051601 PACS number(s): 03.75. Hh, 05.30.Rt, 31.15.xm, 37.30.+i Ultracold atoms coupled to the radiation field of an optical resonator form a long-range interacting many-body system [1-4] that proved to be suitable for the quantum simulation of the superradiant quantum phase transition of the Dicke model [5][6][7]. Critical behavior in nonequilibrium phase transitions between stationary phases of an open system [8][9][10][11][12][13][14][15][16] cannot be cast in the usual formalism of the symmetry-breaking transition of the ground state. As it has been predicted [8,9] and recent experiments have proved [17], photon dissipation and the accompanying quantum fluctuations substantially modify the correlation functions and the critical exponents [10,18]. Dissipation is thus a key factor in quantum criticality. In addition, measured data revealed the effect of another dissipation channel related to atomic collisions [17]. In this paper we show that the damping rate of the soft mode can undergo an unexpected, resonancelike, huge enhancement prior to vanishing. The variation of the soft-mode frequency as the control parameter is tuned and the bath composed of the usually neglected phonon degrees of freedom is sampled at different points. At a certain value of the control parameter the spectral mode density diverges and the damping rate gets enhanced.Elementary excitations of a homogeneous Bose-Einstein condensate of ultracold atoms are collective density waves with different wave numbers that can be considered quasiparticles. Besides the dispersion relation, the quasiparticles are characterized by a damping rate [19][20][21][22][23][24]. The finite lifetime originates from two possible scattering processes among quasiparticles. The first one leads to Landau damping [25][26][27], where the selected excitation, together with another thermally excited one, merges into a third excitation of the system. This mechanism needs a thermal occupation of the other excitation, therefore it vanishes at zero temperature. In the second, so-called Beliaev damping process [28,29], the selected excitation decays directly into two lower-energy excitations. This scattering process is the basic source of dissipation in a superfluid near zero temperature [30]. In the following, we will consider the Landau and Beliaev collisional decay processes of quasiparticles when the homogeneous Bose gas is in an optical resonator.Suppose that a Bose-Einstein condensate of atoms is placed into an optical resonator [31] and is illuminated by a coherent laser light from the side perpendicular to the cavity axis (see Fig. 1). The laser frequency ω L is far detuned from all atomic tr...