Photonic tuning of Beliaev damping in a superfluid

Kónya, G.; Szirmai, G.; Nagy, Dávid; Domokos, P.

doi:10.1103/physreva.89.051601

Cited by 13 publications

(24 citation statements)

References 40 publications

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“…In fact, recent numerical calculations on this model [50] suggested a different scaling relation n ∼ N α , with α = 0.41, in contrast to the present analysis.…”

Section: A Scaling Analysiscontrasting

confidence: 54%

Keldysh approach for nonequilibrium phase transitions in quantum optics: Beyond the Dicke model in optical cavities

et al. 2013

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We investigate non-equilibrium phase transitions for driven atomic ensembles, interacting with a cavity mode, coupled to a Markovian dissipative bath. In the thermodynamic limit and at low-frequencies, we show that the distribution function of the photonic mode is thermal, with an effective temperature set by the atom-photon interaction strength. This behavior characterizes the static and dynamic critical exponents of the associated superradiance transition. Motivated by these considerations, we develop a general Keldysh path integral approach, that allows us to study physically relevant nonlinearities beyond the idealized Dicke model. Using standard diagrammatic techniques, we take into account the leading-order corrections due to the finite number of atoms N. For finite N, the photon mode behaves as a damped, classical non-linear oscillator at finite temperature. For the atoms, we propose a Dicke action that can be solved for any N and correctly captures the atoms' depolarization due to dissipative dephasing.

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“…In fact, recent numerical calculations on this model [50] suggested a different scaling relation n ∼ N α , with α = 0.41, in contrast to the present analysis.…”

Section: A Scaling Analysiscontrasting

confidence: 54%

Keldysh approach for nonequilibrium phase transitions in quantum optics: Beyond the Dicke model in optical cavities

et al. 2013

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“…For example, in the above-quoted experimental realization there is another dissipation channel acting on the spin component of the system, which was shown to have a significant influence on the measured correlation functions [21]. Based on a microscopic calculation beyond the Bogoliubov approach, the observed damping has been attributed to a Beliaev-type damping process in the superfluid with a highly non-trivial spectrum of the phonon reservoir at low frequencies [23,24].We consider a bosonic two-mode model in which one of the modes is coupled to a simple Markovian bath whereas the other one is subjected to a colored reservoir. This general model describes with high accuracy the normal phase of the Dicke-type phase transition [9].…”

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confidence: 94%

Nonequilibrium Quantum Criticality and Non-Markovian Environment: Critical Exponent of a Quantum Phase Transition

Nagy

Domokos

2015

Phys. Rev. Lett.

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We show that the critical exponent of a quantum phase transition in a damped-driven open system is determined by the spectral density function of the reservoir. We consider the open-system variant of the Dicke model, where the driven boson mode and also the large N-spin couple to independent reservoirs at zero temperature. The critical exponent, which is 1 if there is no spin-bath coupling, decreases below 1 when the spin couples to a sub-Ohmic reservoir.PACS numbers: 05.30. Rt,42.50.Pq,37.10.Vz,37.30.+i Quantum critical behavior appears in driven dissipative systems when the steady-state [1][2][3], rather than the ground state of a Hamiltonian [4][5][6], undergoes a nonanalytic, symmetry-breaking change at a critical parameter value. The interplay of an external coherent excitation and the dissipation can lead to a steady-state which is far from the ground or thermal state. Driven dissipative systems cannot be, in general, mapped onto an effective Hamiltonian system. It is thus unclear how the critical behavior of the open system is related to universality classes of known quantum and thermal phase transitions [7].Recent observation of the Dicke-model superradiant phase transition motivates us to raise this question. Ultracold atoms coupled to the radiation field of an optical resonator allowed for the quantum simulation of the Dicke model [8][9][10] and the experimental demonstration of the phase transition [10][11][12][13][14][15][16]. The boson component of the model is represented by a single mode of a high finesse optical cavity. The spin-N component is effectively realized by constraining the motion of ultracold atoms into the space of two momentum eigenstates. The interaction is implemented by a far-detuned laser field illuminating the atoms from a direction perpendicular to the cavity axis. Photons scatter into the cavity, which has a recoil on the atoms. Above a threshold of the laser intensity, which translates to the coupling strength between the spin and the boson mode, a mean field of the cavity mode and the large spin is formed spontaneously.Since the cavity mode is coupled through the mirrors to the outside electromagnetic vacuum field, this system is intrinsically open. It is also a substantial feature that the coupling between cavity photons and atoms is generated by an external laser. In the frame rapidly rotating at the laser frequency, the time-dependent driving can be eliminated and the remaining low-frequency dynamics is described by the time-independent Dicke-type Hamiltonian [9,10,17]. Note, however, that the outcoupled field is continuously supplied by the external laser and a photon current is driven through the system. According to the effective Hamiltonian, the incoherent photon population in the ground state diverges at the critical point as a power law with exponent 1/2 [18]. At variance, when the cavity loss is taken into account [19,20], the exponent changes to 1 which is much closer to the experimentally measured value of about 0.9 [21]. The dissipation and the accompanying q...

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“…[52]. The damping rate enhancement can be attributed to the interaction with the other density-wave modes of the condensate via s-wave collision.…”

Section: Introductionmentioning

confidence: 99%

Damping of quasiparticles in a Bose-Einstein condensate coupled to an optical cavity

2014

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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.

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Photonic tuning of Beliaev damping in a superfluid

Cited by 13 publications

References 40 publications

Keldysh approach for nonequilibrium phase transitions in quantum optics: Beyond the Dicke model in optical cavities

Keldysh approach for nonequilibrium phase transitions in quantum optics: Beyond the Dicke model in optical cavities

Nonequilibrium Quantum Criticality and Non-Markovian Environment: Critical Exponent of a Quantum Phase Transition

Damping of quasiparticles in a Bose-Einstein condensate coupled to an optical cavity

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