Refine
Year of publication
Document Type
- Article (58)
- Preprint (3)
- Part of a Book (1)
Language
- English (62)
Keywords
The Tavis-Cummings model is a paradigmatic central-mode model in which a set of two-level quantum emitters (spins) are coupled to a collective cavity mode. Here we study the eigenstate spectrum, its localization properties, and the effect on dynamics, focusing on the two-excitation sector relevant for nonlinear photonics. These models admit two sources of disorder: in the coupling between the spins and the cavity, and in the energy shifts of the individual spins. While this model was known to be exactly solvable in the limit of a homogeneous coupling and inhomogeneous energy shifts, we establish here the solvability in the opposite limit of a homogeneous energy shift and inhomogeneous coupling, presenting the exact solution and corresponding conserved quantities. We identify three different classes of eigenstates, exhibiting different degrees of multifractality and semilocalization closely tied to the integrable points, and we study their stability to perturbations away from these solvable points. The dynamics of the cavity occupation number away from equilibrium, exhibiting boson bunching and a two-photon blockade, is explicitly related to the localization properties of the eigenstates, and it illustrates how these models support a collective spin description despite the presence of disorder.
Quantum superpositions of macroscopically distinguishable states having distinct phases can be created with a Bose-Einstein condensate trapped in a periodic potential. The experimental signature is contained in the phase distribution of the interference patterns obtained after releasing the traps. Moreover, in the double-well case, this distribution exhibits a dramatic dependence on the parity of the total number of atoms. We finally show that, for single-well occupations up to a few hundred atoms, the macroscopic quantum superposition can be robust enough against decoherence to be experimentally revealable within current technology.
We study superfluid dissipation due to phase slips for a Bose-Einstein condensate flowing through a repulsive barrier inside a torus. The barrier is adiabatically raised across the annulus, while the condensate flows with a finite quantized angular momentum. At a critical height, a vortex moves from the inner region and reaches the barrier to eventually circulate around the annulus. At a higher critical height, an antivortex also enters into the torus from the outer region. Both vortex and antivortex decrease the total angular momentum by leaving behind a 2π phase slip. When they collide and annihilate or orbit along the same loop, the condensate suffers a global 2π phase slip, and the total angular momentum decreases by one quantum. In hydrodynamic regime, the instability sets in when the local superfluid velocity equals the sound speed inside the barrier region.
We investigate the problem of an ultracold atomic gas in the superfluid phase flowing in the presence of a potential barrier or a periodic potential. We use a hydrodynamic scheme in the local density approximation (LDA) to obtain an analytic expression for the critical current as a function of the barrier height or the lattice intensity, which applies to both Bose and Fermi superfluids. In this scheme, the stationary flow becomes energetically unstable when the local superfluid velocity is equal to the local sound velocity at the point where the external potential is maximum. We compare this prediction with the results of the numerical solutions of the Gross-Pitaevskii and Bogoliubov-de Gennes equations. We discuss the role of long-wavelength excitations in determining the critical velocity. Our results allow one to identify the different regimes of superfluid flow, namely, the LDA hydrodynamic regime, the regime of quantum effects beyond LDA for weak barriers and the regime of tunneling between weakly coupled superfluids for strong barriers. We finally discuss the relevance of these results in the context of current experiments with ultracold gases.
We study the current-phase relation of a Bose-Einstein condensate flowing through a repulsive square barrier by solving analytically the one-dimensional Gross-Pitaevskii equation. The barrier height and width fix the current-phase relation j(δϕ), which tends to j~cos(δϕ/2) for weak barriers and to the Josephson sinusoidal relation j~sin(δϕ) for strong barriers. Between these two limits, the current-phase relation depends on the barrier width. In particular, for wide-enough barriers, we observe two families of multivalued current-phase relations. Diagrams belonging to the first family, already known in the literature, can have two different positive values of the current at the same phase difference. The second family, new to our knowledge, can instead allow for three different positive currents still corresponding to the same phase difference. Finally, we show that the multivalued behavior arises from the competition between hydrodynamic and nonlinear-dispersive components of the flow, the latter due to the presence of a soliton inside the barrier region.
Rabi interferometry and sensitive measurement of the Casimir-Polder force with ultracold gases
(2010)
We show that Rabi oscillations of a degenerate fermionic or bosonic gas trapped in a double-well potential can be exploited for the interferometric measurement of external forces at micrometer length scales. The Rabi interferometer is less sensitive but easier to implement than the Mach-Zehnder, since it does not require dynamical beam-splitting or recombination processes. As an application we propose a measurement of the Casimir-Polder force acting between the atoms and a dielectric surface. We find that even if the interferometer is fed with a coherent state of relatively small number of atoms, and in the presence of realistic experimental noise, the force might be measured with a sensitivity sufficient to discriminate between thermal and zero-temperature regimes of the Casimir-Polder potential. Higher sensitivities can be reached with bosonic spin squeezed states.
We investigate how to estimate from atom-position measurements the relative phase of two Bose-Einstein condensates released from a double-well potential. We demonstrate that the phase-estimation sensitivity via the fit of the average density to the interference pattern is fundamentally bounded by shot noise. The shot noise can be overcome by estimating the phase from the measurement of order √N (or higher) correlation functions. The optimal estimation strategy, saturating the quantum Fisher information, requires the measurement of the Nth-order correlation function. We demonstrate that a different estimation method—based on the detection of the center of mass of the interference pattern—also provides sub-shot-noise sensitivity. The implementation of both protocols, however, might be experimentally challenging.
Instability and vortex ring dynamics in a three-dimensional superfluid flow through a constriction
(2011)
We study the instability of a superfluid flow through a constriction in three spatial dimensions. We consider a Bose–Einstein condensate at zero temperature in two different geometries: a straight waveguide and a torus. The constriction consists of a broad, repulsive penetrable barrier. In the hydrodynamic regime, we find that the flow becomes unstable as soon as the velocity at the classical (Thomas–Fermi) surface equals the sound speed inside the constriction. At this critical point, vortex rings enter the bulk region of the cloud. The nucleation and dynamics scenario is strongly affected by the presence of asymmetries in the velocity and density of the background condensate flow.
We study the population dynamics of a Bose-Einstein condensate in a double-well potential throughout the crossover from Josephson dynamics to hydrodynamics. At barriers higher than the chemical potential, we observe slow oscillations well described by a Josephson model. In the limit of low barriers, the fundamental frequency agrees with a simple hydrodynamic model, but we also observe a second, higher frequency. A full numerical simulation of the Gross-Pitaevskii equation giving the frequencies and amplitudes of the observed modes between these two limits is compared to the data and is used to understand the origin of the higher mode. Implications for trapped matter-wave interferometers are discussed.
We derive the asymptotic maximum-likelihood phase estimation uncertainty for any interferometric protocol where the positions of the probe particles are measured to infer the phase, but where correlations between the particles are not accessible. First, we apply our formula to the estimation of the phase acquired in the Mach–Zehnder interferometer and recover the well-known momentum formula for the phase sensitivity. Then, we apply our results to interferometers with two spatially separated modes, which could be implemented with a Bose–Einstein condensate trapped in a double-well potential. We show that in a simple protocol which estimates the phase from an interference pattern, a sub-shot-noise phase uncertainty of up to Δθ∝N−2/3 can be achieved. One important property of this estimation protocol is that its sensitivity does not depend on the value of the phase θ, contrary to the sensitivity given by the momentum formula for the Mach–Zehnder transformation. Finally, we study the experimental implementation of the above protocol in detail, by numerically simulating the full statistics as well as by considering the main sources of detection noise, and argue that the shot-noise limit could be surpassed with current technology.
Self-ordered limit cycles, chaos, and phase slippage with a superfluid inside an optical resonator
(2015)
We study dynamical phases of a driven Bose-Einstein condensate coupled to the light field of a high-Q optical cavity. For high field seeking atoms at red detuning the system is known to show a transition from a spatially homogeneous steady state to a self-ordered regular lattice exhibiting superradiant scattering into the cavity. For blue atom pump detuning the particles are repelled from the maxima of the light-induced optical potential suppressing scattering. We show that this generates a new dynamical instability of the self-ordered phase, leading to the appearance of self-ordered stable limit cycles characterized by large amplitude self-sustained oscillations of both the condensate density and cavity field. The limit cycles evolve into chaotic behavior by period doubling. Large amplitude oscillations of the condensate are accompanied by phase slippage through soliton nucleation at a rate that increases in the chaotic regime. Different from a superfluid in a closed setup, this driven dissipative superfluid is not destroyed by the proliferation of solitons since kinetic energy is removed through cavity losses.
Coherent scattering of light from ultracold atoms involves an exchange of energy and momentum introducing a wealth of nonlinear dynamical phenomena. As a prominent example, particles can spontaneously form stationary periodic configurations that simultaneously maximize the light scattering and minimize the atomic potential energy in the emerging optical lattice. Such self-ordering effects resulting in periodic lattices via bimodal symmetry breaking have been experimentally observed with cold gases and Bose-Einstein condensates (BECs) inside an optical resonator. Here, we study a new regime of periodic pattern formation for an atomic BEC in free space, driven by far off-resonant counterpropagating and noninterfering lasers of orthogonal polarization. In contrast to previous works, no spatial light modes are preselected by any boundary conditions and the transition from homogeneous to periodic order amounts to a crystallization of both light and ultracold atoms breaking a continuous translational symmetry. In the crystallized state the BEC acquires a phase similar to a supersolid with an emergent intrinsic length scale whereas the light field forms an optical lattice allowing phononic excitations via collective backscattering, which are gapped due to the infinte-range interactions. The system we study constitutes a novel configuration allowing the simulation of synthetic solid-state systems with ultracold atoms including long-range phonon dynamics.
We study the late-time relaxation following a quench in an open quantum many-body system. We consider the open Dicke model, describing the infinite-range interactions between N atoms and a single, lossy electromagnetic mode. We show that the dynamical phase transition at a critical atom-light coupling is characterized by the interplay between reservoir-driven and intrinsic relaxation processes in the absence of number conservation. Above the critical coupling, small fluctuations in the occupation of the dominant quasiparticle mode start to grow in time, while the quasiparticle lifetime remains finite due to losses. Near the critical interaction strength, we observe a crossover between exponential and power-law 1/τ relaxation, the latter driven by collisions between quasiparticles. For a quench exactly to the critical coupling, the power-law relaxation extends to infinite times, but the finite lifetime of quasiparticles prevents aging from appearing in two-times response and correlation functions. We predict our results to be accessible to quench experiments with ultracold bosons in optical resonators.
We propose an enhanced optical interferometer based on tailored non-classical light generated by nonlinear dynamics and projective measurements in a three-level atom cavity QED system. A coherent state in the cavity becomes dynamically entangled with two ground states of the atom and is transformed to a macroscopic superposition state via a projective measurement on the atom. We show that the resulting highly non-classical state can improve interferometric precision measurements well beyond the shot-noise limit once combined with a classical laser pulse at the input of a Mach–Zehnder interferometer. For a practical implementation, we identify an efficient phase shift estimation scheme based on the counting of photons at the interferometer output. Photon losses and photon-counting errors deteriorate the interferometer sensitivity, but we demonstrate that it still can be significantly better than the shot-noise limit under realistic conditions.
The non-linear coupled particle light dynamics of an ultracold gas in the field of two independent counter-propagating laser beams can lead to the dynamical formation of a self-ordered lattice structure as presented in (2016) Phys. Rev. X 6 021026. Here we present new numerical studies on experimentally observable signatures to monitor the growth and properties of such a crystal in real time. While, at least theoretically, optimal non-destructive observation of the growth dynamics and the hallmarks of the crystalline phase can be performed by analyzing scattered light, monitoring the evolution of the particle's momentum distribution via time-of-flight probing is an experimentally more accessible choice. In this work we show that both approaches allow us to unambiguously distinguish the crystal from independent collective scattering as it occurs in matter wave super-radiance. As a clear crystallization signature, we identify spatial locking between the two emerging standing laser waves, together creating the crystal potential. For sufficiently large systems, the system allows reversible adiabatic ramping into the crystalline phase as an alternative to a quench across the phase transition and growth from fluctuations.
Collective excitations and supersolid behavior of bosonic atoms inside two crossed optical cavities
(2017)
We discuss the nature of symmetry breaking and the associated collective excitations for a system of bosons coupled to the electromagnetic field of two optical cavities. For the specific configuration realized in a recent experiment at ETH [1, 2], we show that, in absence of direct intercavity scattering and for parameters chosen such that the atoms couple symmetrically to both cavities, the system possesses an approximate U(1) symmetry which holds asymptotically for vanishing cavity field intensity. It corresponds to the invariance with respect to redistributing the total intensity $I={I}_{1}+{I}_{2}$ between the two cavities. The spontaneous breaking of this symmetry gives rise to a broken continuous translation-invariance for the atoms, creating a supersolid-like order in the presence of a Bose–Einstein condensate. In particular, we show that atom-mediated scattering between the two cavities, which favors the state with equal light intensities ${I}_{1}={I}_{2}$ and reduces the symmetry to ${{\bf{Z}}}_{2}\otimes {{\bf{Z}}}_{2}$, gives rise to a finite value $\sim \sqrt{I}$ of the effective Goldstone mass. For strong atom driving, this low energy mode is clearly separated from an effective Higgs excitation associated with changes of the total intensity I. In addition, we compute the spectral distribution of the cavity light field and show that both the Higgs and Goldstone mode acquire a finite lifetime due to Landau damping at non-zero temperature.
We consider a spinless ultracold Fermi gas tightly trapped along the axis of an optical resonator and transversely illuminated by a laser closely tuned to a resonator mode. At a certain threshold pump intensity, the homogeneous gas density breaks a Z2 symmetry towards a spatially periodic order, which collectively scatters pump photons into the cavity. We show that this known self-ordering transition also occurs for low field seeking fermionic particles when the laser light is blue detuned to an atomic transition. The emergent superradiant optical lattice in this case is homopolar and possesses two distinct dimerizations. Depending on the spontaneously chosen dimerization, the resulting Bloch bands can have a nontrivial topological structure characterized by a nonvanishing Zak phase. In the case where the Fermi momentum is close to half of the cavity-mode wave number, a Peierls-like instability here creates a topological insulator with a gap at the Fermi surface, which hosts a pair of edge states. The topological features of the system can be nondestructively observed via the cavity output: the Zak phase of the bulk coincides with the relative phase between laser and cavity field, while the fingerprint of edge states can be observed as additional broadening in a well-defined frequency window of the cavity spectrum.
We study spatial spin and density self-ordering of a two-component Bose-Einstein condensate via collective Raman scattering into a linear cavity mode. The onset of the Dicke superradiance phase transition is marked by a simultaneous appearance of a crystalline density order and a spin-wave order. The latter spontaneously breaks the discrete Z2 symmetry between even and odd sites of the cavity optical potential. Moreover, in the superradiant state the continuous U(1) symmetry of the relative phase of the two condensate wave functions is explicitly broken by the cavity-induced position-dependent Raman coupling with a zero spatial average. Thus, the spatially averaged relative condensate phase is locked at either π/2 or −π/2. This continuous symmetry breaking and relative condensate phase locking by a zero-average Raman field can be considered as a generic order-by-disorder process similar to the random-field-induced order in the two-dimensional classical ferromagnetic XY spin model. However, the seed of the random field in our model stems from quantum fluctuations in the cavity field and is a dynamical entity affected by self-ordering. The spectra of elementary excitations exhibit the typical mode softening at the superradiance threshold.
Supersolids are characterized by the counterintuitive coexistence of superfluid and crystalline order. Here we study a supersolid phase emerging in the steady state of a driven-dissipative system. We consider a transversely pumped Bose-Einstein condensate trapped along the axis of a ring cavity and coherently coupled to a pair of degenerate counterpropagating cavity modes. Above a threshold pump strength the interference of photons scattered into the two cavity modes results in an emergent superradiant lattice, which spontaneously breaks the continuous translational symmetry towards a periodic atomic pattern. The crystalline steady state inherits the superfluidity of the Bose-Einstein condensate, thus exhibiting genuine properties of a supersolid. A gapless collective Goldstone mode correspondingly appears in the superradiant phase, which can be nondestructively monitored via the relative phase of the two cavity modes on the cavity output. Despite cavity-photon losses the Goldstone mode remains undamped, indicating the robustness of the supersolid phase.
We consider the d-dimensional transverse-field Ising model with power-law interactions J/rd+σ in the presence of a noisy longitudinal field with zero average. We study the longitudinal-magnetization dynamics of an initial paramagnetic state after a sudden switch-on of both the interactions and the noisy field. While the system eventually relaxes to an infinite-temperature state with vanishing magnetization correlations, we find that two-time correlation functions show aging at intermediate times. Moreover, for times shorter than the inverse noise strength κ and distances longer than a(J/κ)2/σ with a being the lattice spacing, we find a critical scaling regime of correlation and response functions consistent with the model A dynamical universality class with an initial-slip exponent θ=1 and dynamical critical exponent z=σ/2. We obtain our results analytically by deriving an effective action for the magnetization field including the noise in a nonperturbative way. The above scaling regime is governed by a nonequilibrium fixed point dominated by the noise fluctuations.
