We show that a Bose-Hubbard model with local loss exhibits a first-order dark-state phase transition between a dark soliton and a uniform superfluid. Semiclassical simulations and stability analysis reveal that the soliton acts as a many-body dark state, whose suppressed fluctuations modify the transition relative to the comparable phenomenon of optical bistability in Kerr resonators. This mechanism quantitatively captures the bistable phase boundary observed in the experiment of Labouvie [], resolving long-standing discrepancies in previous theoretical modeling. Our results identify a general route by which spatial coherence and engineered loss can generate nonequilibrium phase transitions in ultracold gases.
We show that a Bose-Hubbard model with local loss exhibits a first-order dark-state phase transition between a dark soliton and a uniform superfluid. Semiclassical simulations and stability analysis reveal that the soliton acts as a many-body dark state, whose suppressed fluctuations modify the transition relative to the comparable phenomenon of optical bistability in Kerr resonators. This mechanism quantitatively captures the bistable phase boundary observed in the experiment of Labouvie [], resolving long-standing discrepancies in previous theoretical modeling. Our results identify a general route by which spatial coherence and engineered loss can generate nonequilibrium phase transitions in ultracold gases.
Over the past decades ultracold atomic gases have emerged as a highly controllable platform for probing quantum many-body phenomena, including Bose-Einstein condensation and superfluidity. These systems are particularly suited to exploring the physics of open quantum systems where interactions with the environment, traditionally considered a source of decoherence, can be engineered to reveal new types of non-equilibrium behaviour. This thesis focuses on the dissipative Josephson array, a setup of ultracold atoms subjected to a controlled loss mechanism. The primary goal is to better understand a series of intriguing experimental observations by analysing a range of theoretical models. As such, the focus is put on the dissipative Bose-Hubbard model, which isolates the lattice dynamics and provides insight into the system’s steady-state properties. Our analysis reveals qualitative similarities to the rather simple picture of a Kerr resonator, but also points to significant differences. To refine our understanding, we develop an effective model for the internal reservoirs based on incoherent driving, which accurately captures the observed non-equilibrium steady states. Additionally, signs of a previously unexplored region in phase space are observed. The work culminates in the identification of this phase: the standing dark soliton. Using a detailed 3D model, we reconstruct the system’s full phase diagram and perform a direct comparison with experimental data, demonstrating the relevance of the dark soliton to the observed phenomena.
We investigate the effects of phase noise and particle loss on the dynamics of a Bose-Einstein condensate in an optical lattice. Starting from the many-body master equation, we discuss the applicability of generalized mean-field approximations in the presence of dissipation as well as methods to simulate quantum effects beyond mean field by including higher-order correlation functions. It is shown that localized particle dissipation leads to surprising dynamics, as it can suppress decay and restorethe coherence of a Bose-Einstein condensate. These effects can be applied to engineer coherent structures such as stable discrete breathers and dark solitons.
We present a fully quantum many-body treatment of dark solitons formed by ultracold bosonic atoms in one-dimensional optical lattices. Using time-evolving block decimation to simulate the single-band Bose-Hubbard Hamiltonian, we consider the quantum dynamics of density and phase engineered dark solitons as well as the quantum evolution of mean-field dark solitons injected into the quantum model. The former approach directly models how one may create quantum entangled dark solitons in experiment. While we have already presented results regarding the latter approach elsewhere [R. V. Mishmash and L. D. Carr, Phys. Rev. Lett. 103, 140403 (2009)], we expand upon those results in this work. In both cases, quantum fluctuations cause the dark soliton to fill in and may induce an inelasticity in soliton-soliton collisions. Comparisons are made to the Bogoliubov theory which predicts depletion into an anomalous mode that fills in the soliton. Our many-body treatment allows us to go beyond the Bogoliubov approximation and calculate explicitly the dynamics of the system's natural orbitals.
The recent experimental realisation of Bose–Fermi superfluid mixtures of dilute ultracold atomic gases has opened new perspectives in the study of quantum many-body systems. Depending on the values of the scattering lengths and the amount of bosons and fermions, a uniform Bose–Fermi mixture is predicted to exhibit a fully mixed phase, a fully separated phase or, in addition, a purely fermionic phase coexisting with a mixed phase. The occurrence of this intermediate configuration has interesting consequences when the system is nonuniform. In this work we theoretically investigate the case of solitonic solutions of coupled Bogoliubov–de Gennes and Gross–Pitaevskii equations for the fermionic and bosonic components, respectively. We show that, in the partially separated phase, a dark soliton in Fermi superfluid is accompanied by a broad bosonic component in the soliton, forming a dark–bright soliton which keeps full spatial coherence.
Dark solitons of ultracold bosons in the vicinity of the Mott-insulator--superfluid phase transition are studied. Making use of the Gutzwiller ansatz we have found antisymmetric eigenstates corresponding to standing solitons, as well as propagating solitons created by phase imprinting. Near the phase boundary, superfluidity has either a particle or a hole character depending on the system parameters, which greatly affects the characteristics of both types of solitons. Within the insulating Mott regions, soliton solutions are prohibited by lack of phase coherence between the lattice sites. Linear and modulational stability show that the soliton solutions are sensitive to small perturbations and, therefore, unstable. In general, their lifetimes differ for on-site and off-site modes. For the on-site modes, there are small areas between the Mott-insulator regions where the lifetime is very large, and in particular much larger than that for the off-site modes.
We study, both analytically and numerically, the formation and propagation of dark solitons in a superfluid Fermi gas in the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC). Starting from a superfluid order-parameter equation, we derive a Korteweg--de Vries equation for weak nonlinear excitations under quasi-one-dimensional and long-wavelength approximations. We present dark soliton solutions valid for both BCS and BEC limits and also for the crossover, and show that dark solitons in different superfluid regimes possess different features. Particularly, a dark soliton in the BCS (BEC) regime has larger (smaller) propagating velocity and smaller (larger) spatial width. Upon moving to the boundary of the condensate, it generally decelerates and generates small radiations, which display different behavior in different superfluid regimes. We study also a head-on collision between two dark solitons and demonstrate that the phase shift due to the collision changes nonmonotonically along the BCS-BEC crossover. All analytical results are checked by numerical simulations, and good agreement between them is found.