We investigate how to describe the dissipative spin dynamics of the driven-dissipative Dicke model, describing N two-level atoms coupled to a cavity mode, after adiabatic elimination of the cavity mode. To this end, we derive a Redfield master equation which goes beyond the standard secular approximation and large detuning limits. We show that the secular (or rotating wave) approximation and the large detuning approximation both lead to inadequate master equations, that fail to predict the Dicke transition or the damping rates of the atomic dynamics. In contrast, the full Redfield theory correctly predicts the phase transition and the effective atomic damping rates. Our work provides a reliable framework to study the full quantum dynamics of atoms in a multimode cavity, where a quantum description of the full model becomes intractable.

We investigate multiqubit permutation-symmetric states with maximal entropy of entanglement. Such states can be viewed as particular spin states, namely anticoherent spin states. Using the Majorana representation of spin states in terms of points on the unit sphere, we analyze the consequences of a point-group symmetry in their arrangement on the quantum properties of the corresponding state. We focus on the identification of anticoherent states (for which all reduced density matrices in the symmetric subspace are maximally mixed) associated with point-group symmetric sets of points. We provide three different characterizations of anticoherence, and establish a link between point symmetries, anticoherence and classes of states equivalent through stochastic local operations with classical communication (SLOCC). We then investigate in detail the case of small numbers of qubits, and construct infinite families of anticoherent states with point-group symmetry of their Majorana points, showing that anticoherent states do exist to arbitrary order.

We derive a markovian master equation for the internal dynamics of an ensemble of two-level atoms including all effects related to the quantization of their motion. Our equation provides a unifying picture of the consequences of recoil and indistinguishability of atoms beyond the Lamb-Dicke regime on both their dissipative and conservative dynamics, and applies equally well to distinguishable and indistinguishable atoms. We give general expressions for the decay rates and the dipole-dipole shifts for any motional states, and we find closed-form formulas for a number of relevant states (Gaussian states, Fock states and thermal states). In particular, we show that dipole-dipole interactions and cooperative photon emission can be modulated through the external state of motion.

Capturing non-Markovian dynamics of open quantum systems is generally a challenging problem, especially for strongly interacting many-body systems. In this Letter, we combine recently developed non-Markovian quantum state diffusion techniques with tensor network methods to address this challenge. As a first example, we explore a Hubbard-Holstein model with dissipative phonon modes, where this new approach allows us to quantitatively assess how correlations spread in the presence of non-Markovian dissipation in a 1D many-body system. We find regimes where correlation growth can be enhanced by these effects, offering new routes for dissipatively enhancing transport and correlation spreading, relevant for both solid state and cold atom experiments.

Inspired by the microscopic control over dissipative processes in quantum optics and cold atoms, we develop an open-system framework to study dissipative control of transport in strongly interacting fermionic systems, relevant for both solid state and cold atom experiments. We show how subgap currents exhibiting Multiple Andreev Reflections -the stimulated transport of electrons in the presence of Cooper-pairs -can be controlled via engineering of superconducting leads or superfluid atomic gases. Our approach incorporates dissipation within the channel, which is naturally occurring and can be engineered in cold gas experiments. This opens opportunities for engineering many phenomena with transport in strongly interacting systems. As examples, we consider particle loss and dephasing, and note different behaviour for currents with different microscopic origin. We also show how to induce nonreciprocal electron and Cooper-pair currents.Introduction. Understanding and controlling the outof-equilibrium dynamics of strongly interacting manybody systems constitutes one of the key forefronts in quantum physics across a variety of subfields in experiment and theory. In this context, opportunities to achieve their control via dissipation mechanisms have arisen [1,2], as is applied for few-body systems in quantum optics [3,4]. This is especially true in cold-atom platforms, where large separations between frequency scales allows well-controlled theoretical models and implementations of dissipative processes, as realized for laser cooling and trapping [5]. The longer timescales of cold atom experiments also allow dynamics to be tracked and potentially controlled time-dependently [6,7]. Outof-equilibrium transport dynamics remain a ubiquitous paradigm in the solid state [8], and recent developments in cold atom systems have also made it possible to engineer quantised transport of atoms between reservoirs, as well as quantum point contacts and waveguides [9][10][11][12]. Here we explore the emerging new opportunity of using dissipation engineering to achieve control of quantum transport properties, that are relevant for both coldatom and solid-state platforms.

We investigate superradiance and subradiance of indistinguishable atoms with quantized motional states, starting with an initial total state that factorizes over the internal and external degrees of freedom of the atoms. Due to the permutational symmetry of the motional state, the cooperative spontaneous emission, governed by a recently derived master equation [F. Damanet et al., Phys. Rev. A 93, 022124 (2016)], depends only on two decay rates γ and γ0 and a single parameter ∆ dd describing the dipole-dipole shifts. We solve the dynamics exactly for N = 2 atoms, numerically for up to 30 atoms, and obtain the large-N -limit by a mean-field approach. We find that there is a critical difference γ0 − γ that depends on N beyond which superradiance is lost. We show that exact non-trivial dark states (i.e. states other than the ground state with vanishing spontaneous emission) only exist for γ = γ0, and that those states (dark when γ = γ0) are subradiant when γ < γ0.

We propose and analyze a mechanism for rectification of spin transport through a small junction between two spin baths or leads. For interacting baths we show that transport is conditioned on the spacial asymmetry of the quantum junction mediating the transport, and attribute this behavior to a gapped spectral structure of the lead-system-lead configuration. For non-interacting leads a minimal quantum model that allows for spin rectification requires an interface of only two interacting two-level systems. We obtain approximate results with a weak-coupling Born-masterequation in excellent agreement with matrix-product-state calculations that are extrapolated in time by mimicking absorbing boundary conditions. These results should be observable in controlled spin systems realized with cold atoms, trapped ions, or in electrons in quantum dot arrays.

Semiconductor heterostructures [1] and ultracold neutral atomic lattices [2] capture many of the essential properties of onedimensional (1D) electronic systems. However, fully 1D superlattices are highly challenging to fabricate in the solid state due to the inherently small length scales involved. Conductive atomic-force microscope (c-AFM) lithography applied to an oxide interface can create ballistic few-mode electron waveguides with highly quantized conductance and strongly attractive electron-electron interactions [3]. Here we show that artificial Kronig-Penney-like superlattice potentials can be imposed on such waveguides, introducing a new superlattice spacing that can be made comparable to the mean separation between electrons. The imposed superlattice potential fractures the electronic subbands into a manifold of new subbands with magnetically-tunable fractional conductance. The lowest plateau, associated with ballistic transport of spin-singlet electron pairs [3], shows enhanced electron pairing, in some cases up to the highest magnetic fields explored. A 1D model of the system suggests that an engineered spin-orbit interaction in the superlattice contributes to the enhanced pairing observed in the devices. These findings are an advance in the ability to design new families of quantum materials with emergent properties and the development of solid-state 1D quantum simulation platforms.Quantum theory provides a unified framework for understanding the fundamental properties of matter.However, there are many quantum systems whose behavior is not well understood because the relevant equations are are not able to be solved using known approaches. The idea of "quantum simulation", first articulated by Feynman [4], aims to exploit the quantum-mechanical properties of materials to compute the properties of interest and gain insight into the quantum nature of matter. There are two main "flavors" of quantum simulation: one based upon the known efficiency of circuit-based quantum computers to solve the Schrödinger equation, and the other based on microscopic control over quantum systems to emulate a given Hamiltonian. The former approach is limited by the capabilities of present-day quantum computers. The latter approach has shown great promise using a variety of methods including ultracold atoms [2, 5, 6], spin systems from ion trap arrays [7]. superconducting Josephson junction arrays [8], photonic systems [9], and various solid-state approaches [1,10,11,12]. Platforms capable of quantum simulation of Hubbard models would be of enormous value in condensed matter physics and beyond.Complex oxides offer new opportunities to create a platform for quantum simulation in a solid-state