arXiv subjects

Simon B. Jäger

Publications and source records attributed to Simon B. Jäger.

47 records · Page 3Linked to original sources

arXiv2020

Regular and bistable steady-state superradiant phases of an atomic beam traversing an optical cavity

We investigate the different photon emission regimes created by a preexcited and collimated atomic beam passing through a single mode of an optical cavity. In the regime where the cavity degrees of freedom can be adiabatically eliminated, we find that the atoms undergo superradiant emission when the collective linewidth exceeds the transit-time broadening. We analyze the case where the atomic beam direction is slanted with respect to the cavity axis. For this situation, we find that a phase of continuous light emission similar to steady-state superradiance is established providing the tilt of the atomic beam is sufficiently small. However, if the atoms travel more than half a wavelength along the cavity axis during one transit time we predict a dynamical phase transition to a new bistable superradiant regime. In this phase the atoms undergo collective spontaneous emission with a frequency that can be either blue or red detuned from the free-space atomic resonance. We analyze the different superradiant regimes and the quantum critical crossover boundaries. In particular we find the spectrum of the emitted light and show that the linewidth exhibits features of a critical scaling close to the phase boundaries.

quant-ph↗

arXiv2020

Edge states of the long-range Kitaev chain: an analytical study

We analyze the properties of the edge states of the one-dimensional Kitaev model with long-range anisotropic pairing and tunneling. Tunneling and pairing are assumed to decay algebraically with exponents $α$ and $β$, respectively, and $α,β>1$. We determine analytically the decay of the edges modes. We show that the decay is exponential for $α=β$ and when the coefficients scaling tunneling and pairing terms are equal. Otherwise, the decay is exponential at sufficiently short distances and then algebraic at the asymptotics. We show that the exponent of the algebraic tail is determined by the smallest exponent between $α$ and $β$. Our predictions are in agreement with numerical results found by exact diagonalization and in the literature.

cond-mat.str-el↗

arXiv2019

Superradiant optomechanical phases of cold atomic gases in optical resonators

We theoretically analyze superradiant emission of light from a cold atomic gas, when mechanical effects of photon-atom interactions are considered. The atoms are confined within a standing-wave resonator and an atomic metastable dipolar transition couples to a cavity mode. The atomic dipole is incoherently pumped in the parameter regime that would correspond to stationary superradiance in absence of inhomogeneous broadening. Starting from the master equation for cavity field and atomic degrees of freedom we derive a mean-field model that allows us to determine a threshold temperature, above which thermal fluctuations suppress superradiant emission. We then analyze the dynamics of superradiant emission when the motion is described by a mean-field model. In the semiclassical regime and below the threshold temperature we observe that the emitted light can be either coherent or chaotic, depending on the incoherent pump rate. We then analyze superradiant emission from an ideal Bose gas at zero temperature when the superradiant decay rate $Λ$ is of the order of the recoil frequency $ω_R$. We show that the quantized exchange of mechanical energy between the atoms and the field gives rise to a threshold, $Λ_c$, below which superradiant emission is damped down to zero. When $Λ>Λ_c$ superradiant emission is accompanied by the formation of matter-wave gratings diffracting the emitted photons. The stability of these gratings depends on the incoherent pump rate $w$ with respect to a second threshold value $w_c$. For $w>w_c$ the gratings are stable and the system achieves stationary superradiance. Below this second threshold the coupled dynamics becomes chaotic. We characterize the dynamics across these two thresholds and show that the three phases we predict (incoherent, coherent, chaotic) can be revealed via the coherence properties of the light at the cavity output.

cond-mat.quant-gas↗

arXiv2019

Dynamical phase transitions to optomechanical superradiance

We theoretically analyze superradiant emission of light from an ultracold gas of bosonic atoms confined in a bad cavity. A metastable dipolar transition of the atoms couples to the cavity field and is incoherently pumped, the mechanical effects of cavity-atom interactions tend to order the atoms in the periodic cavity potential. By means of a mean-field model we determine the conditions on the cavity parameters and pump rate that lead to the buildup of a stable macroscopic dipole emitting coherent light. We show that this occurs when the superradiant decay rate and the pump rate exceed threshold values of the order of the photon recoil energy. Above these thresholds superradiant emission is accompanied by the formation of stable matter-wave gratings that diffract the emitted photons. Outside of this regime, instead, the optomechanical coupling can give rise to dephasing or chaos, for which the emitted light is respectively incoherent or chaotic. These behaviors exhibit the features of a dynamical phase transitions and emerge from the interplay between global optomechanical interactions, quantum fluctuations, and noise.

quant-ph↗

arXiv2017

Quenches across the self-organization transition in multimode cavities

A cold dilute atomic gas in an optical resonator can be radiatively cooled by coherent scattering processes when the driving laser frequency is tuned close but below the cavity resonance. When sufficiently illuminated, moreover, the atoms' steady state undergoes a phase transition from homogeneous density to crystalline order. We characterize the dynamics of this self-ordering process in the semi-classical regime when distinct cavity modes with commensurate wavelengths are quasi-resonantly driven by laser fields via scattering by the atoms. The lasers are simultaneously applied and uniformly illuminate the atoms, their frequencies are chosen so that the atoms are cooled by the radiative processes, their intensity is either suddenly switched or slowly ramped across the self-ordering transition. Numerical simulations for different ramp protocols predict that the system exhibits long-lived metastable states, whose occurrence strongly depends on initial temperature, ramp speed, and number of atoms.

quant-ph↗

arXiv2017

Phases of cold atoms interacting via photon-mediated long-range forces

Atoms in high-finesse optical resonators interact via the photons they multiply scatter into the cavity modes. The dynamics is characterized by dispersive and dissipative optomechanical long-range forces, which are mediated by the cavity photons, and exhibits a steady state for certain parameter regimes. In standing-wave cavities the atoms can form stable spatial gratings. Moreover, their asymptotic distribution is a Maxwell-Boltzmann whose effective temperature is controlled by the laser parameters. In this work we show that in a two-mode standing-wave cavity the stationary state possesses the same properties and phases of the Generalized Hamiltonian Mean Field model in the canonical ensemble. This model has three equilibrium phases: a paramagnetic, a nematic, and a ferromagnetic one, which here correspond to different spatial orders of the atomic gas and can be detected by means of the light emitted by the cavities. We further discuss perspectives for investigating in this setup the ensemble inequivalence predicted for the Generalized Hamiltonian Mean Field model.

quant-ph↗

arXiv2017

Semiclassical theory of synchronization-assisted cooling

We analyse the dynamics leading to radiative cooling of an atomic ensemble confined inside an optical cavity when the atomic dipolar transitions are incoherently pumped and can synchronize. Our study is performed in the semiclassical regime and assumes that cavity decay is the largest rate in the system dynamics. We identify three regimes characterising the cooling. At first hot atoms are individually cooled by the cavity friction forces. After this stage, the atoms' center-of-mass motion is further cooled by the coupling to the internal degrees of freedom while the dipoles synchronize. In the latest stage dipole-dipole correlations are stationary and the center-of-mass motion is determined by the interplay between friction and dispersive forces due to the coupling with the collective dipole. We analyse this asymptotic regime by means of a mean-field model and show that the width of the momentum distribution can be of the order of the photon recoil. Furthermore, the internal excitations oscillate spatially with the cavity standing wave forming an antiferromagnetic-like order.

quant-ph↗

arXiv2016

Dissipation-assisted prethermalization in long-range interacting atomic ensembles

We theoretically characterize the semiclassical dynamics of an ensemble of atoms after a sudden quench across a driven-dissipative second-order phase transition. The atoms are driven by a laser and interact via conservative and dissipative long-range forces mediated by the photons of a single-mode cavity. These forces can cool the motion and, above a threshold value of the laser intensity, induce spatial ordering. We show that the relaxation dynamics following the quench exhibits a long prethermalizing behaviour which is first dominated by coherent long-range forces, and then by their interplay with dissipation. Remarkably, dissipation-assisted prethermalization is orders of magnitude longer than prethermalization due to the coherent dynamics. We show that it is associated with the creation of momentum-position correlations, which remain nonzero for even longer times than mean-field predicts. This implies that cavity cooling of an atomic ensemble into the selforganized phase can require longer time scales than the typical experimental duration. In general, these results demonstrate that noise and dissipation can substantially slow down the onset of thermalization in long-range interacting many-body systems.

quant-ph↗

arXiv2016

Mean-field theory of atomic self-organization in optical cavities

Photons mediate long-range optomechanical forces between atoms in high finesse resonators, which can induce the formation of ordered spatial patterns. When a transverse laser drives the atoms, the system undergoes a second order phase transition, that separates a uniform spatial density from a Bragg grating maximizing scattering into the cavity and is controlled by the laser intensity. Starting from a Fokker-Planck equation describing the semiclassical dynamics of the $N$-atom distribution function, we systematically develop a mean-field model and analyse its predictions for the equilibrium and out-of-equilibrium dynamics. The validity of the mean-field model is tested by comparison with the numerical simulations of the $N$-body Fokker-Planck equation and by means of a BBGKY hierarchy. The mean-field theory predictions well reproduce several results of the $N$-body Fokker-Planck equation for sufficiently short times, and are in good agreement with existing theoretical approaches based on field-theoretical models. Mean-field, on the other hand, predicts thermalization time scales which are at least one order of magnitude shorter than the ones predicted by the $N$-body dynamics. We attribute this discrepancy to the fact that the mean-field ansatz discards the effects of the long-range incoherent forces due to cavity losses.

quant-ph↗

arXiv2015

Thermodynamics and dynamics of atomic self-organization in an optical cavity

Pattern formation of atoms in high-finesse optical resonators results from the mechanical forces of light associated with superradiant scattering into the cavity mode. It occurs when the laser intensity exceeds a threshold value, such that the pumping processes counteract the losses. We consider atoms driven by a laser and coupling with a mode of a standing-wave cavity and describe their dynamics with a Fokker-Planck equation, in which the atomic motion is semiclassical but the cavity field is a full quantum variable. The asymptotic state of the atoms is a thermal state, whose temperature is solely controlled by the detuning between the laser and the cavity frequency and by the cavity loss rate. From this result we derive the free energy and show that in the thermodynamic limit selforganization is a second-order phase transition. The order parameter is the field inside the resonator, to which one can associate a magnetization in analogy to ferromagnetism, the control field is the laser intensity, however the steady state is intrinsically out-of-equilibrium. In the symmetry-broken phase quantum noise induces jumps of the spatial density between two ordered patterns: We characterize the statistical properties of this temporal behaviour at steady state and show that the thermodynamic properties of the system can be extracted by detecting the light at the cavity output. The results of our analysis are in full agreement with previous studies, extend them by deriving a self-consistent theory which is valid also when the cavity field is in the shot-noise limit, and elucidate the nature of the selforganization transition.

quant-ph↗

arXiv2015

Supercooling of Atoms in an Optical Resonator

We investigate laser cooling of an ensemble of atoms in an optical cavity. We demonstrate that when atomic dipoles are sychronized in the regime of steady-state superradiance, the motion of the atoms may be subject to a giant frictional force leading to potentially very low temperatures. The ultimate temperature limits are determined by a modified atomic linewidth, which can be orders of magnitude smaller than the cavity linewidth. The cooling rate is enhanced by the superradiant emission into the cavity mode allowing reasonable cooling rates even for dipolar transitions with ultranarrow linewidth.

quant-ph↗