We describe the dynamics of two component non-interacting ultracold Fermions which are initially in thermal equilibrium and undergo a rapid quench to either the repulsive or attractive side of a Feshbach resonance. The short time dynamics is dominated by the exponentially growing collective modes. We study the Stoner instability and formation of ferromagnetic textures on the repulsive side, and the pairing instability towards BCS or FFLO-like states (determined by the population imbalance) on the attractive side. In each case, we evaluate the growth rate of unstable modes and predict the typical lengthscale of textures to be formed.
We study the coherent non-equilibrium dynamics of interacting two-dimensional systems after a quench from a trivial to a topological Chern insulator phase. While the many-body wavefunction is constrained to remain topologically trivial under local unitary evolution, we find that the Hall response of the system can dynamically approach a thermal value of the post-quench Hamiltonian, even though the efficiency of this thermalization process is shown to strongly depend on the microscopic form of the interactions. Quite remarkably, the effective temperature of the steady state Hall response can be…
Using a Luttinger liquid theory we investigate the time evolution of the particle density of a one-dimensional fermionic system with open boundaries and subject to a finite duration quench of the inter-particle interaction. We provide analytical and asymptotic solutions to the unitary time evolution of the system, showing that both switching on and switching off the quench ramp create light-cone perturbations in the density. The post-quench dynamics is strongly affected by the interference between these two perturbations. In particular, we find that the discrepancy between the time-dependent d…
We report on the observation of a quenched moment of inertia as resulting from superfluidity in a strongly interacting Fermi gas. Our method is based on setting the hydrodynamic gas in slow rotation and determining its angular momentum by detecting the precession of a radial quadrupole excitation. The measurements distinguish between the superfluid or collisional origin of hydrodynamic behavior, and show the phase transition.
We consider the quantum evolution of a pair of interacting atoms in a three dimensional isotropic trap where the interaction strength is quenched from one value to another. Using exact solutions of the static problem we are able to evaluate time-dependent observables such as the overlap between initial and final states and the expectation value of the separation between the two atoms. In the case where the interaction is quenched from the non-interacting regime to the strongly interacting regime, or vice versa, we are able to obtain analytic results. Examining the overlap between the initial a…
Reaching a target quantum state from an initial state within a finite temporal window is a challenging problem due to non-adiabaticity. We study the optimal protocol for swithcing on interactions to reach the ground state of a weakly interacting Luttinger liquid within a finite time $τ$, starting from the non-interacting ground state. The protocol is optimized by minimizing the excess energy at the end of the quench, or by maximizing the overlap with the interacting ground state. We find that the optimal protocol is symmetric with respect to $τ/2$, and can be expressed as a functional of the o…
We explore the dynamics of a Bose gas following its quench to a strongly interacting regime near a Feshbach resonance. Within a self-consistent Bogoliubov analysis we find that after the initial condensate-quasiparticle Rabi oscillations, at long time scales the gas is characterized by a nonequilibrium steady-state momentum distribution function, with depletion, condensate density and contact that deviate strongly from their corresponding equilibrium values. These are in a qualitative agreement with recent experiments on Rb85 by Makotyn, et al. Our analysis also suggests that for sufficiently …
In a recent work by Gong and Ueda (arXiv:1710.05289), the classification of (1+1)-dimensional quench dynamics for the ten Altland-Zirnbauer classes is achieved, and entanglement-spectrum crossings of the time-dependent states for the topological classes (AIII, DIII, CII, BDI, and D) are discovered as a consequence of the bulk-edge correspondence. We note that, their classification scheme relies on the limit that the energy spectrum of the post-quench Hamiltonian is flat, because any finite band dispersion leads to the break down of time-reversal and chiral symmetries for the parent Hamiltonian…
We obtain an exact expression for the time evolution of the interacting Bose gas following a quench from a generic initial state using the Yudson representation for integrable systems. We study the time evolution of the density and noise correlation for a small number of bosons and their asymptotic behavior for any number. We show that for any value of the coupling, as long as it is repulsive, the system asymptotes towards a strongly repulsive gas, while for any value of an attractive coupling the long time behavior is dominated by the maximal bound state. This occurs independently of the init…
We study the response of a particle current to dissipative dephasing in an interacting, few-body fermionic lattice system. The particles are prepared in the ground state in presence of an artificial magnetic gauge field, which is subsequently quenched to zero. The initial current decays non-trivially in the dissipative environment and we explore the emerging dynamics and its dependence on various system parameters.
Many-body systems driven out of equilibrium can exhibit scaling flows of the quantum state. For a sudden quench to resonant interactions between particles we construct a new class of analytical scaling solutions for the time evolved wave function with a complex scale parameter. These solutions determine the exact dynamical scaling of observables such as the pair correlation function, the contact and the fidelity. We give explicit examples of the nonequilibrium dynamics for two trapped fermions or bosons quenched to unitarity, for ideal Bose polarons, and for resonantly interacting, Borromean t…
We report on the dynamical formation of exceptional degeneracies in basic correlation functions of non-integrable one- and two-dimensional systems quenched to the vicinity of a critical point. Remarkably, fine-tuned semi-metallic points in the phase diagram of the considered systems are thereby promoted to topologically robust non-Hermitian (NH) nodal phases emerging in the coherent long-time evolution of a dynamically equilibrating system. In the framework of non-equilibrium Green's function methods within the conserving second Born approximation, we predict observable signatures of these nov…
Multipartite entanglement, such as witnessed through the quantum Fisher information (QFI), is a crucial resource for quantum technologies, but its experimental certification is highly challenging. Here, we propose an experimentally friendly protocol to measure the QFI. It relies on recording the short-time dynamics of simple observables after a quench from a thermal state, works for spins, bosons, and fermions, and can be implemented in standard cold-atom experiments and other platforms with temporal control over the system Hamiltonian. To showcase the protocol, we simulate it for the one-dime…
We show that the dynamics of quenches in one dimension far off equilibrium can be described by power laws, but with exponents differing from the fully renormalized ones at lowest energies. Instead they depend on the initial state and its excitation energy. Furthermore, we found that for quenches to strong interactions unexpected similarities between systems in one and in infinite dimensions occur, indicating the dominance of local processes.
We study the early-time dynamics of a degenerate Bose gas after a sudden quench of the interaction strength, starting from a weakly interacting gas. By making use of a time-dependent generalization of the Nozières-Saint-James variational formalism, we describe the crossover of the early-time dynamics from shallow to deep interaction quenches. We analyze the coherent oscillations that characterize both the density of excited states and the Tan's contact as a function of the final scattering length. For shallow quenches, the oscillatory behaviour is negligible and the dynamics is universally gov…
The dynamics of the Luttinger model after a quantum quench is studied. We compute in detail one and two-point correlation functions for two types of quenches: from a non-interacting to an interacting Luttinger model and vice-versa. In the former case, the non-interacting Fermi gas features in the momentum distribution and other correlation functions are destroyed as time evolves. In the infinite-time limit, equal-time correlations are power-laws but the critical exponents are found to differ from their equilibrium values. In all cases, we find that these correlations are well described by a ge…
Recently, it has been shown that the momentum distribution of a metallic state of fermionic atoms in a lattice Fermi-Bose mixture exhibits coherent oscillations after a global quench that suppresses tunneling. The oscillation period is determined by the Fermi-Bose interaction strength. Here we show that similar dynamics occurs in the fermionic Hubbard model when we quench a noninteracting metallic state by introducing a Hubbard interaction and suppressing tunneling. The period is determined primarily by the interaction strength. Conversely, we show that one can accurately determine the Hubbard…
We study the quench dynamics of a one-dimensional ultracold Fermi gas in an optical lattice potential with synthetic spin-orbit coupling. At equilibrium, the ground state of the system can undergo a topological phase transition and become a topological superfluid with Majorana edge states. As the interaction is quenched near the topological phase boundary, we identify an interesting dynamical phase transition of the quenched state in the long-time limit, characterized by an abrupt change of the pairing gap at a critical quenched interaction strength. We further demonstrate the topological natu…
Although most studies of strongly correlated systems away from equilibrium have focused on clean systems, it is well known that disorder may significantly modify observed properties in various nontrivial ways. The nonequilibrium interplay of interaction and disorder in these systems thus requires further investigation. In the present paper, we use the recently developed nonequilibrium DMFT+CPA embedding scheme, that combines both the dynamical mean field theory (DMFT) and the coherent potential approximation (CPA) nonequilibrium extensions, to characterize the relaxation and the thermalization…
We analyze the static and dynamical properties of a one-dimensional topological lattice, the fermionic Su-Schrieffer-Heeger model, in the presence of on-site interactions. Based on a study of charge and spin correlation functions, we elucidate the nature of the topological edge modes, which depending on the sign of the interactions, either display particles of opposite spin on opposite edges, or a pair and a holon. This study of correlation functions also highlights the strong entanglement that exists between the opposite edges of the system. This last feature has remarkable consequences upon …
Using the time-dependent density matrix renormalization group method and exact diagonalization, we study the non-equilibrium dynamics of the one-dimensional Fermi-Hubbard model following a quantum quench or a ramp of the onsite interaction strength. For quenches from the non-interacting to the attractive regime, we investigate the dynamical emergence of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) correlations, which at finite spin polarizations are the dominant two-body correlations in the ground state, and their signatures in the pair quasi-momentum distribution function. We observe that the post…
We present a non-equilibrium Green's functional approach to study the dynamics following a quench in weakly interacting Bose Hubbard model (BHM). The technique is based on the self-consistent solution of a set of equations which represents a particular case of the most general set of Hedin's equations for the interacting single-particle Green's function. We use the ladder approximation as a skeleton diagram for the two-particle scattering amplitude useful, through the self-energy in the Dyson equation, for finding the interacting single-particle Green's function. This scheme is then implemente…
We study a nonequilibrium dynamics of a one-dimensional spin-imbalanced Fermi-Hubbard model following a quantum quench of on-site interaction, realizable, for example, in Feshbach-resonant atomic Fermi gases. We focus on the post-quench evolution starting from the initial BCS and FuldeFerrell-Larkin-Ovchinnikov (FFLO) ground states and analyze the corresponding spin-singlet, spin-triplet, density-density, and magnetization-magnetization correlation functions. We find that beyond a light-cone crossover time, rich post-quench dynamics leads to thermalized and pre-thermalized stationary states th…
We present an experimental study of a two component Fermi gas following an interaction quench into the superfluid phase. Starting with a weakly attractive gas in the normal phase, interactions are ramped to unitarity at a range of rates and we measure the subsequent dynamics as the gas approaches equilibrium. Both the formation and condensation of fermion pairs are mapped via measurements of the pair momentum distribution and can take place on very different timescales, depending on the adiabaticity of the quench. The contact parameter is seen to respond very quickly to changes in the interact…
Quantum simulation with ultracold atoms has become a powerful technique to gain insight into interacting many-body systems. In particular, the possibility to study nonequilibrium dynamics offers a unique pathway to understand correlations and excitations in strongly interacting quantum matter. So far, coherent nonequilibrium dynamics has exclusively been observed in ultracold many-body systems of bosonic atoms. Here we report on the observation of coherent quench dynamics of fermionic atoms. A metallic state of ultracold spin-polarised fermions is prepared along with a Bose-Einstein condensate…
We consider a system of non-interacting fermions in one dimension subject to a single-particle potential consisting of (a) a strong optical lattice, (b) a harmonic trap, and (c) uncorrelated on-site disorder. After a quench, in which the center of the harmonic trap is displaced, we study the occupation function of the fermions and the time-evolution of experimental observables. Specifically, we present numerical and analytical results for the post-quench occupation function of the fermions, and analyse the time-evolution of the real-space density profile. Unsurprisingly for a non-interacting (…
We study the relaxation dynamics of interacting, one-dimensional fermions with band curvature after a weak quench in the interaction parameter. After the quench, the system is described by a non-equilibrium initial state, which relaxes towards thermal equilibrium, featuring prethermal behavior on intermediate time and length scales. The model corresponds to the class of interacting Luttinger Liquids, which extends the quadratic Luttinger theory by a weak integrability breaking phonon scattering term. In order to solve for the non-equilibrium time evolution, we use kinetic equations for the pho…
Near a continuous phase transition, systems with different microscopic origins display universal dynamics if their underlying symmetries are compatible. In a thermally quenched system, the Kibble-Zurek mechanism for the creation of topological defects unveils this universality through a characteristic power-law exponent, which captures the dependence of the defect density on the quench rate. Here, we report the observation of the Kibble-Zurek universality in a strongly interacting Fermi superfluid. As the system's microscopic description is tuned from bosonic to fermionic, the quench formation…
We study the effect of suddenly turning on a long-range interaction in a spinless Fermi gas in two dimensions. The short to intermediate time dynamics is obtained using the method of bosonization of the Fermi surface. This allow to calculate the full space-time dependence of the non-equilibrium fermion density matrix as well as the evolution of the quasiparticle residue after the quench. It is thus found that the asymptotic state predicted by bosonization is consistent with the prethermalized state. From the bosonized representation, we explicitly construct the Generalized Gibbs Ensamble that …
The Higgs amplitude mode of the order parameter of an ultracold confined Fermi gas in the BCS regime after a quench of the coupling constant is analyzed theoretically. Characteristic features are a damped oscillation which at a certain transition time changes into a rather irregular dynamics. We compare the numerical solution of the full set of nonlinear equations of motion for the normal and anomalous Bogoliubov quasiparticle excitations with a linearized approximation. In doing so the transition time as well as the difference between resonant systems, i.e., systems where the Fermi energy is …
We study the dynamics of interacting superfluid bosons in a one dimensional vertical optical lattice after a sudden increase of the lattice potential depth. We show that this system can be exploited to investigate the effects of strong interactions on Bloch oscillations. We perform theoretical modelling of this system, identify experimental challenges and explore a new regime of Bloch oscillations characterized by interaction-induced matter-wave collapse and revivals which modify the Bloch oscillations dynamics. In addition, we study three dephasing mechanisms: effective three-body interaction…
Spontaneous symmetry breaking occurs in a physical system whenever the ground state does not share the symmetry of the underlying theory, e.g., the Hamiltonian. It gives rise to massless Nambu-Goldstone modes and massive Anderson-Higgs modes. These modes provide a fundamental understanding of matter in the Universe and appear as collective phase/amplitude excitations of an order parameter in a many-body system. The amplitude excitation plays a crucial role in determining the critical exponents governing universal non-equilibrium dynamics in the Kibble-Zurek mechanism (KZM). Here, we characteri…
By exploring a phase space hydrodynamics description of one-dimensional free Fermi gas, we discuss how systems settle down to steady states described by the generalized Gibbs ensembles through quantum quenches. We investigate time evolutions of the Fermions which are trapped in external potentials or a circle for a variety of initial conditions and quench protocols. We analytically compute local observables such as particle density and show that they always exhibit power law relaxation at late times. We find a simple rule which determines the power law exponent. Our findings are, in principle,…
The absence of a characteristic momentum scale in the pseudo-potential description of atomic interaction in ultracold (two-component Fermi) gases is known to lead to divergence in perturbation theory. Here we show that they also plague the calculation of the dynamics of the total energy following a quantum quench. A procedure to remove the divergence is devised, which provides finite answers for the time-evolution of the total energy after a quench in which the interaction strength is ramped up according to an arbitrary protocol. An important result of this analysis is the time evolution of th…
We study the pairing dynamics of polar states in a single species p-wave superfluid Fermi gas following a sudden change of the interaction strength. The anisotropy of pair interaction together with the presence of the centrifugal barrier results in profoundly different pairing dynamics compared to the s-wave case. Depending on the direction of quenches, quench to the BCS regime results in a large oscillatory depletion of momentum occupation inside the Fermi sea or a large filling of momentum occupation. We elucidate a crucial role of the resonant state supported by the centrifugal barrier in t…
We present a numerical study of a confined ultracold Fermi gas showing that the Goldstone mode of the BCS gap is directly visible in the dynamics of the single-particle excitations. To this end, we investigate the low-energy dynamic response of a confined Fermi gas to a rapid change of the scattering length (i.e., an interaction quench). Based on a fully microscopic time-dependent density-matrix approach within the Bogoliubov-de Gennes formalism that includes a 3D harmonic confinement we simulate and identify the emergence of the Goldstone mode in a cigar-shaped $^6$Li gas. We show that the qu…
We theoretically study the out-of-equilibrium dynamics in momentum space of a weakly interacting disordered Bose gas launched with a finite velocity. In the absence of interactions, coherent multiple scattering gives rise to a background of diffusive particles, on top of which a coherent backscattering interference emerges. We revisit this scenario in the presence of interactions, using a diagrammatic quantum transport theory. We find that the dynamics is governed by coupled kinetic equations describing the thermalization of the diffusive and coherent components of the gas. This phenomenon lea…
We study a system of few fermions in a one-dimensional harmonic trap, and focus on the case of dipolar majority particles in contact with a single impurity. The impurity is used both for quenching the system, and for tracking the system evolution after the quench. Employing exact diagonalization, we investigate relaxation and thermalization properties. In the absence of dipolar interactions, the system is near integrability, and the dynamics remains oscillatory even on long time scales. On the other hand, repulsive as well as attractive dipolar interactions lead to quick relaxation to the diag…
We unravel the ground state properties and the non-equilibrium quantum dynamics of two bosonic impurities immersed in an one-dimensional fermionic environment by applying a quench of the impurity-medium interaction strength. In the ground state, the impurities and the Fermi sea are phase-separated for strong impurity-medium repulsions while they experience a localization tendency around the trap center for large attractions. We demonstrate the presence of attractive induced interactions mediated by the host for impurity-medium couplings of either sign and analyze the competition between induce…
The properties of prototypical examples of one-dimensional fermionic systems undergoing a sudden quantum quench from a gapless state to a (partially) gapped state are analyzed. By means of a Generalized Gibbs Ensemble analysis or by numerical solutions in the interacting cases, we observe an anomalous, non-monotonic response of steady state correlation functions as a function of the strength of the mechanism opening the gap. In order to interpret this result, we calculate the full dynamical evolution of these correlation functions, which shows a freezing of the propagation of the quench inform…
Using a Fermi-Bose mixture of ultra-cold atoms in an optical lattice, we construct a quantum simulator for a U(1) gauge theory coupled to fermionic matter. The construction is based on quantum links which realize continuous gauge symmetry with discrete quantum variables. At low energies, quantum link models with staggered fermions emerge from a Hubbard-type model which can be quantum simulated. This allows us to investigate string breaking as well as the real-time evolution after a quench in gauge theories, which are inaccessible to classical simulation methods.
We consider a weakly interacting uniform atomic Bose gas with a time-dependent nonlinear coupling constant. By developing a suitable Bogoliubov treatment we investigate the time evolution of several observables, including the momentum distribution, the degree of coherence in the system, and their dependence on dimensionality and temperature. We rigorously prove that the low-momentum Bogoliubov modes remain frozen during the whole evolution, while the high-momentum ones adiabatically follow the change in time of the interaction strength. At intermediate momenta we point out the occurrence of os…
We study the dynamics of a one-dimensional Bose gas after a sudden change of the interaction strength from zero to a finite value using the numerical time-evolving block decimation (TEBD) algorithm. It is shown that despite the integrability of the system, local quantities such as the two-particle correlation $g^{(2)}(x,x)$ attain steady state values in a short characteristic time inversely proportional to the Tonks parameter $γ$ and the square of the density. The asymptotic values are very close to those of a finite temperature grand canonical ensemble with a local temperature corresponding t…
We explore the interspecies interaction quench dynamics of ultracold spin-polarized few-body mass balanced Fermi-Fermi mixtures confined in a double-well with an emphasis on the beyond Hartree-Fock correlation effects. It is shown that the ground state of particle imbalanced mixtures exhibits a symmetry breaking of the single-particle density for strong interactions in the Hartree-Fock limit, which is altered within the many-body approach. Quenching the interspecies repulsion towards the strongly interacting regime the two species phase separate within the Hartree-Fock approximation while rema…
We theoretically investigate the magnetic properties and nonequilibrium dynamics of two interacting ultracold polar and paramagnetic molecules in a one-dimensional harmonic trap in external electric and magnetic fields. The molecules interact via a multichannel two-body contact potential, incorporating the short-range anisotropy of intermolecular interactions. We show that various magnetization states arise from the interplay of the molecular interactions, electronic spins, dipole moments, rotational structures, external fields, and spin-rotation coupling. The rich magnetization diagrams depen…
We consider non-equilibrium dynamics of two initially independent reservoirs $A$ and $B$ filled with a cold Fermi gas coupled and decoupled by two quantum quenches following one another. We find that the von Neumann entropy production induced by the quench is faster than thermal transport between the reservoirs and defines the short-time dynamics of the system. We analyze the energy change in the system which adds up the heat transferred between $A$ and $B$ and the work done by the quench to uncouple the reservoirs. In the case when $A$ and $B$ interact for a short time, we notice an energy in…
We describe a diabatic protocol to prepare a strongly-interacting Bose-Einstein condensate in a regime where neither an adiabatic ramp nor a direct diabatic quench are desirable. This protocol is expected to achieve a nearly unit population transfer to the strongly-interacting ground state for realistic experimental parameters for $^{85}$Rb. The protocol matches the initial and final density profiles by modifying the trap along with the scattering length during the quench. The protocol should reveal several properties of the strongly-interacting Bose gas, and enable further investigation of be…
Recent exact solutions of the 1D Kardar-Parisi-Zhang equation make use of the 1D integrable Lieb-Liniger model of interacting bosons. For flat initial conditions, it requires the knowledge of the overlap between the uniform state and arbitrary exact Bethe eigenstates. The same quantity is also central in the study of the quantum quench from a 1D non-interacting Bose-Einstein condensate upon turning interactions. We compare recent advances in both domains, i.e. our previous exact solution, and a new conjecture by De Nardis et al.. This leads to new exact results and conjectures for both the qua…
