arXiv subjects

Berislav Buca

Publications and source records attributed to Berislav Buca.

16 recordsLinked to original sources

arXiv2025

UniqueNESS: Graph Theory Approach to the Uniqueness of Non-Equilibrium Stationary States of the Lindblad Master Equation

The dimensionality of kernels for Lindbladian superoperators is of physical interest in various scenarios out of equilibrium, for example in mean-field methods for driven-dissipative spin lattice models that give rise to phase diagrams with a multitude of non-equilibrium stationary states in specific parameter regions. We show that known criteria established in the literature for unique fixpoints of the Lindblad master equation can be better treated in a graph-theoretic framework via a focus on the connectivity of directed graphs associated to the Hamiltonian and jump operators.

quant-ph↗

arXiv2022

Tunable Non-equilibrium Phase Transitions between Spatial and Temporal Order through Dissipation

We propose an experiment with a driven quantum gas coupled to a dissipative optical cavity that realizes a novel kind of far-from-equilibrium phase transition between spatial and temporal order. The control parameter of the transition is the detuning between the drive frequency and the cavity resonance. For negative detunings, the system features a spatially ordered phase, while positive detunings lead to a phase with both spatial order and persistent oscillations, which we call dissipative spatio-temporal lattice. We give numerical and analytical evidence for this superradiant phase transition and show that the spatio-temporal lattice originates from cavity dissipation. In both regimes the atoms are subject to an accelerated transport, either via a uniform acceleration or via abrupt transitions to higher momentum states. Our work provides perspectives for temporal phases of matter that are not possible at equilibrium.

cond-mat.quant-gas↗

arXiv2022

Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation

Synchronization is a phenomenon where interacting particles lock their motion and display non-trivial dynamics. Despite intense efforts studying synchronization in systems without clear classical limits, no comprehensive theory has been found. We develop such a general theory based on novel necessary and sufficient algebraic criteria for persistently oscillating eigenmodes (limit cycles) of time-independent quantum master equations. We show these eigenmodes must be quantum coherent and give an exact analytical solution for all such dynamics in terms of a dynamical symmetry algebra. Using our theory, we study both stable synchronization and metastable/transient synchronization. We use our theory to fully characterise spontaneous synchronization of autonomous systems. Moreover, we give compact algebraic criteria that may be used to prove absence of synchronization. We demonstrate synchronization in several systems relevant for various fermionic cold atom experiments.

quant-ph↗

arXiv2020

Quantum many-body attractors

Complex dynamics when occurring autonomously, i.e. without external driving, is usually associated with everyday length scales and classical physics, e.g. living organisms. This dynamics is \emph{not} quantum coherent. Quantum coherent dynamics is, by contrast, assumed to be either simple periodic oscillation in particular when autonomous, e.g. spin precession, or random quantum fluctuations. Combining autonomous complex and quantum coherent dynamics on microscopic length-scales could allow for novel coherent quantum machines working without external time-dependent driving. Motivated by this, here we provide an exact theoretical condition for a system to display complex quantum coherent dynamics on both microscopic and macroscopic length scales that we call a \emph{dynamical quantum algebraic thread} (D-QAT). Due to D-QATs our autonomous quantum coherent dynamics is robust to realistic imperfections (including low-doped disorder) and present for generic initial states, allowing for potential realisations in experiments. We give an example of a \emph{spin lace} model structurally similar to magnetic azurite and certain recently experimentally realized large single-molecular magnets with long coherence times. Our work opens the possibility for many potential applications including ultra-dense storage and manipulation of quantum memories, creating \emph{giant} quantum coherent qubits, or microscopic quantum mechanism perform complicated motion.

quant-ph↗

arXiv2020

Dissipative Bethe Ansatz: Exact Solutions of Quantum Many-Body Dynamics Under Loss

We use the Bethe Ansatz technique to study dissipative systems experiencing loss. The method allows us to exactly calculate the Liouvillian spectrum. This opens the possibility of analytically calculating the dynamics of a wide range of experimentally relevant models including cold atoms subjected to one and two body losses, coupled cavity arrays with bosons escaping the cavity, and cavity quantum electrodynamics. As an example of our approach we study the relaxation properties in a boundary driven XXZ spin chain. We exactly calculate the Liouvillian gap and find different relaxation rates with a novel type of dynamical dissipative phase transition. This physically translates into the formation of a stable domain wall in the easy-axis regime despite the presence of loss. Such analytic results have previously been inaccessible for systems of this type.

cond-mat.stat-mech↗

arXiv2019

Dissipation Induced Nonstationarity in a Quantum Gas

Non-stationary long-time dynamics was recently observed in a driven two-component Bose-Einstein condensate coupled to an optical cavity [N. Dogra, et al. arXiv:1901.05974] and analyzed in mean-field theory. We solve the underlying model in the thermodynamic limit and show that this system is always dynamically unstable -- even when mean-field theory predicts stability. Instabilities always occur in higher-order correlation functions leading to squeezing and entanglement induced by cavity dissipation. The dynamics may be understood as the formation of a dissipative time crystal. We use perturbation theory for finite system sizes to confirm the non-stationary behaviour.

quant-ph↗

arXiv2019

The isolated Heisenberg magnet as a quantum time crystal

We demonstrate analytically and numerically that the paradigmatic model of quantum magnetism, the Heisenberg XXZ spin chain, does not relax to stationarity and hence constitutes a genuine time crystal that does not rely on external driving or coupling to an environment. We trace this phenomenon to the existence of extensive dynamical symmetries and find their frequency to be a no-where continuous (fractal) function of the anisotropy parameter of the chain. We discuss how the ensuing persistent oscillations that violate one of the most fundamental laws of physics could be observed experimentally and identify potential metrological applications.

cond-mat.stat-mech↗

arXiv2019

Symmetries and Conservation Laws in Quantum Trajectories: Dissipative Freezing

In driven-dissipative systems, the presence of a strong symmetry guarantees the existence of several steady states belonging to different symmetry sectors. Here we show that, when a system with a strong symmetry is initialized in a quantum superposition involving several of these sectors, each individual stochastic trajectory will randomly select a single one of them and remain there for the rest of the evolution. Since a strong symmetry implies a conservation law for the corresponding symmetry operator on the ensemble level, this selection of a single sector from an initial superposition entails a breakdown of this conservation law at the level of individual realizations. Given that such a superposition is impossible in a classical, stochastic trajectory, this is a a purely quantum effect with no classical analogue. Our results show that a system with a closed Liouvillian gap may exhibit, when monitored over a single run of an experiment, a behaviour completely opposite to the usual notion of dynamical phase coexistence and intermittency, which are typically considered hallmarks of a dissipative phase transition. We discuss our results with a simple, realistic model of squeezed superradiance.

quant-ph↗

arXiv2019

Heating-Induced Long-Range $η$-Pairing in the Hubbard Model

We show how, upon heating the spin degrees of freedom of the Hubbard model to infinite temperature, the symmetries of the system allow the creation of steady-states with long-range correlations between $η$-pairs. With induce this heating with either dissipation or periodic driving and evolve the system towards a nonequilibrium steady state, a process which melts all spin order in the system. The steady state is identical in both cases and displays distance-invariant off-diagonal $η$-correlations. These correlations were first recognised in the superconducting eigenstates in Yang's seminal paper [Phys. Rev. Lett 63, 2144 (1989)], which are a subset of our steady states. We show that our results are a consequence of symmetry properties and entirely independent of the microscopic details of the model and the heating mechanism.

quant-ph↗

arXiv2019

Non-stationary coherent quantum many-body dynamics through dissipation

The assumption that quantum systems relax to a stationary state in the long-time limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate thermalization hypothesis. When an environment is present the expectation is that all of phase space is explored, eventually leading to stationarity. Notable exceptions are decoherence-free subspaces that have important implications for quantum technologies and have so far only been studied for systems with a few degrees of freedom. Here we identify simple and generic conditions for dissipation to prevent a quantum many-body system from ever reaching a stationary state. We go beyond dissipative quantum state engineering approaches towards controllable long-time non-stationarity typically associated with macroscopic complex systems. This coherent and oscillatory evolution constitutes a dissipative version of a quantum time-crystal. We discuss the possibility of engineering such complex dynamics with fermionic ultracold atoms in optical lattices.

quant-ph↗

arXiv2017

Exact matrix product decay modes of a boundary driven cellular automaton

We study integrability properties of a reversible deterministic cellular automaton (the rule 54 of [Bobenko et al., Commun. Math. Phys. 158, 127 (1993)]) and present a bulk algebraic relation and its inhomogeneous extension which allow for an explicit construction of Liouvillian decay modes for two distinct families of stochastic boundary driving. The spectrum of the many-body stochastic matrix defining the time propagation is found to separate into sets, which we call orbitals, and the eigenvalues in each orbital are found to obey a distinct set of Bethe-like equations. We construct the decay modes in the first orbital (containing the leading decay mode) in terms of an exact inhomogeneous matrix product ansatz, study the thermodynamic properties of the spectrum and the scaling of its gap, and provide a conjecture for the Bethe-like equations for all the orbitals and their degeneracy.

cond-mat.stat-mech↗

arXiv2017

Charge and spin current statistics of the open Hubbard model with weak coupling to the environment

Based on generalization and extension of previous work [Phys. Rev. Lett. {\bf 112}, 067201 (2014)] to multiple independent markovian baths we will compute the charge and spin current statistics of the open Hubbard model with weak system-bath coupling up to next-to-leading order in the coupling parameter. The physical results are related to those for the $XXZ$ model in the analogous setup implying a certain universality which potentially holds in this class of nonequilibrium models.

cond-mat.stat-mech↗

arXiv2015

Connected correlations, fluctuations and current of magnetization in the steady state of boundary driven XXZ spin chains

We show how to exploit algebraic relations of operators (or matrices) which constitute the non-equilibrium matrix product steady state of a boundary driven quantum spin chain to find partial differential equations determining all the $m$-point correlation functions in the continuum limit. These partial differential equations, the order of which is determined by scaling of the non-equilibrium partition function, are readily solved if we also know the boundary conditions. In this way we can avoid resorting to representation theory of the matrix product algebra. We apply our methods to study the distributions, or moments, of the magnetization and the spin current observables in boundary driven open XXZ spin chains, as well as some connected correlation functions and find that the transverse connected correlation functions are thermodynamically non-decaying and long-range at the isotropic point $Δ=1$.

cond-mat.stat-mech↗

arXiv2015

Integrable non-equilibrium steady state density operators for boundary driven XXZ spin chains: observables and full counting statistics

We will review some known exact solutions for the steady state of the open quantum Heisenberg $XXZ$ spin chain coupled to a pair of baths [Phys. Rev. Lett. 107, 137201 (2011).]. The dynamics is modelled by the Lindblad master equation. We also review how to calculate some relevant physical observables and provide the statistics of spin current assuming the spin chain is weakly coupled to the baths [Phys. Rev. Lett. 112, 067201 (2014).].

quant-ph↗

arXiv2014

Exactly solvable counting statistics in weakly coupled open interacting spin systems

We study the full counting statistics for interacting quantum many-body spin systems weakly coupled to the environment. In the leading order in the system-bath coupling we derive exact spin current statistics for a large class of parity symmetric spin-1/2 systems driven by a pair of Markovian baths with local coupling operators. Interestingly, in this class of systems the leading order current statistics are universal and do not depend on details of the Hamiltonian. Furthermore, in the specific case of symmetrically boundary driven anisotropic Heisenberg ($XXZ$) spin 1/2 chain we derive explicitly the third-order non-linear corrections to the current statistics.

cond-mat.stat-mech↗

arXiv2012

A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains

We study quantum transport properties of an open Heisenberg XXZ spin 1/2 chain driven by a pair of Lindblad jump operators satisfying a global `microcanonical' constraint, i.e. conserving the total magnetization. We will show that this system has an additional discrete symmetry which is particular to the Liouvillean description of the problem. Such symmetry reduces the dynamics even more than what would be expected in the standard Hilbert space formalism and establishes existence of multiple steady states. Interestingly, numerical simulations of the XXZ model suggest that a pair of distinct non-equilibrium steady states becomes indistinguishable in the thermodynamic limit, and exhibit sub-diffusive spin transport in the easy-axis regime of anisotropy Delta > 1.

quant-ph↗