Session B54: Open Quantum Systems

Thermodynamic observables for AMO systems

Thermodynamic observables are computed by taking a statistical average over all possible system configurations. While the thermalization of a classical system is fairly understood, the counterpart for a quantum system is not true. The goal of this work is to explore the analogue quantum simulation at finite temperature. We study the thermodynamic averaging process to compute the observables, particularly with the Rydberg atom chains. In particular, we consider a spin chain of Rydberg atoms, modeled by the XXZ Hamiltonian, in contact with a bath. We model the system-bath interactions such that they lead to an ensemble of subchains of variable lengths within the spin chain, emulating the grand-canonical averaging process. We use the numerical techniques like the Metropolis scheme and the collisional models to study the nature of the steady states. We highlight the accessibility of the Rydberg interactions for creating an ensemble of subchains, and propose an experimental realization of this construct with the Rydberg atoms.   

Intrinsic mixed-state topological order without quantum memory

Decoherence is a major obstacle to the preparation of topological order in noisy intermediate-scale quantum devices. Here, we show that decoherence can also give rise to new types of topological order. Specifically, we construct two such examples by proliferating fermionic anyons in the two-dimensional toric code model and the Kitaev honeycomb model through certain local quantum channels. The resulting mixed states retain long-range entanglement, which manifests in the nonzero topological entanglement negativity, though the topological quantum memory is destroyed by decoherence. We argue that these properties are stable against perturbations. Therefore, the identified states represent a novel intrinsic mixed-state quantum topological order, which has no counterpart in pure states.   

Exact solutions of boundary driven dissipative quantum spin chains with disorder

Nonequilibrium steady states (NESS) of driven-dissipative quantum spin chains have unique and often surprising properties arising from the interplay of lattice dynamics, driving, and dissipation. Exact solutions are especially valuable to understanding this interplay and the resulting NESS. Here, we derive an exact solution for the steady state of an XX-coupled N-qubit spin chain, with possibly non-uniform couplings, that is subject to a boundary Rabi drive and boundary loss on one end [1]. This model maps to an interacting fermionic model and is thus not amenable to standard techniques to solve for its NESS; however, the model is solvable by exploiting a “hidden” time reversal symmetry in the dissipative dynamics, which allows the model to be solved by creating a doubled version of the system that relaxes into a pure steady state [2]. The model is solvable for a wide range of parameters, including arbitrary non-uniform XX couplings. We show that the non-equilibrium steady state exhibits surprising correlation effects, including an emergent real-space pairing of hole excitations that arises from dynamically constrained hopping. Furthermore, the doubled system is itself is a nontrivial, physically realizable spin chain model whose pure steady state is highly entangled between the two chains. Thus, it provides a means for stabilizing remote multi-qubit entanglement without the use of squeezed light. We outline how this system could be experimentally implemented in e.g., circuit QED or trapped ions. Finally, we discuss extensions of this model.

[1] A. Lingenfelter, et al, arXiv:2307.09482

[2] D. Roberts, et al, PRX Quantum (2021)   

Emergence of self-averaging in non-unitary quench dynamics of chaotic many-body quantum systems

In typical isolated many-body quantum systems, the interplay of interaction and disorder leads to chaos, characterized by correlated eigenvalues and ergodic eigenstates. These features get manifested in the dynamics of the survival probability (overlap of the initial and the time-evolved state) and the spin autocorrelation function in the form of the dip-ramp-plateau structure, also known as the correlation hole. However, the onset of this structure requires large ensemble averages due to the lack of self-averaging of those quantities, i.e. the relative variance of their ensemble averaged value does not decay upon increasing system size. In this presentation, we show that by breaking the unitarity of the time evolution, we induce self-averaging. This is achieved by opening the system and allowing for energy dephasing. We consider three experimental systems to demonstrate the emergence of self-averaging: the one-dimensional disordered Heisenberg chain, the disordered Ising Hamiltonian with long-range interactions, and the non-interacting Anderson model.   

Topologically ordered steady states in open quantum systems

The interplay between dissipation and correlation can lead to new emergent phenomena. Here we study non-equilibrium phases of matter with robust topological degeneracy of steady states, which is a generalization of the ground-state topological degeneracy of closed systems. Specifically, we construct two representative Lindbladians using engineered dissipation, and exactly solve the steady states with topological degeneracy. We find that while the degeneracy is fragile under noise in two dimensions, it is stable in three dimensions, where a genuine many-body phase with topological degeneracy is realized. We identify universal features of dissipative topological physics such as the deconfined emergent gauge field and slow relaxation dynamics of topological defects. The transition from a topologically ordered phase to a trivial phase is also investigated via numerical simulation. Our work highlights the essential difference between ground-state topological order in closed systems and steady-state topological order in open systems.   

Entanglement assisted probe of the non-Markovian to Markovian transition in open quantum system dynamics

We utilize a superconducting qubit processor to experimentally probe the transition from non-Markovian to Markovian dynamics of an open quantum system. We prepare an entangled state between two qubits and monitor the evolution of entanglement over time as one of the qubits interacts with a small quantum environment consisting of a third noisy qubit. We observe the collapse and revival of the entanglement as a signature of quantum memory effects in the environment. We then engineer the quantum memory lifetime to study the transition between non-Markovian and Markovian dynamics, where the environment behaves respectively as a quantum and classical memory.   

Markovian and non-Markovian master equations versus an exactly solvable model of a qubit in a cavity

We investigate the dynamics of a qubit in a leaky cavity interacting with a bosonic bath, using the Jaynes–Cummings model, characterized by three different spectral densities: an impulse spectral density, an Ohmic spectral density, and a proportional spectral density with a sharp cutoff. Specifically, we focus on the behavior of the first excitation state and explore its non-Markovian features, such as oscillatory amplitudes. We derived solutions from various approximation methods to investigate their ability to approximate the exact solution and discuss their optimal performance with respect to relevant parameters. We consider the time-convolutionless (TCL) master equation up to the second order (TCL2) and the fourth order (TCL4), the coarse-graining Lindblad equation (CG-LE), and the rotating-wave approximation Lindblad equation (RWA-LE). Notably, we compare two variants of CG-LE: one based on a completely positive (CP) map that derives the semigroup master equation from first principles and another employing the Born approximation along with bath correlation functions. We obtain the optimal coarse-graining time by optimizing a metric that quantifies the deviation between the approximated and exact solutions. We demonstrate that CG-LE outperforms the Markov limit derived from RWA-LE for the cases of low coupling or high cavity frequency where the Markovian approximation is valid. In the presence of non-Markovian effects characterized by highly oscillatory and non-decaying behavior, the TCL approximation closely matches the exact solution for a short duration. Additionally, for the spectral density with a sharp cutoff, the TCL approximation accurately captures the non-zero asymptotic behavior.   

Title: Oral: Non-Markovian Quantum Emitter Interactions via a Structured Reservoir

Waveguides enable efficient coupling between distant quantum emitters, with nanophotonic structures facilitating engineerable photonic dispersion properties. Dispersion engineering can decrease the speed of light by several orders of magnitude compared to free space, allowing for long-ranged interactions between quantum emitters and exotic many-body light-matter interactions. In such regimes, the dynamics of quantum emitters becomes non-Markovian owing to the memory effects of the slow electromagnetic fields mediating the interaction.

We explore the collective behavior of two distant quantum emitters coupled through a waveguide with nonlinear dispersion properties. We demonstrate the modifications to collective dynamics beyond regular superradiance and subradiance phenomena and discuss the effects of dispersion engineering on the onset of collective behavior. Such waveguide mediated non-Markovian collective atom-field interactions are relevant to distributed quantum sensing and metrology protocols and quantum networks.   

Steady State Convergence Conditions for the Fourth Order Time-Convolutionless Master Equation

Accurately describing the long time behavior of open quantum systems is crucial for modelling how any real system is affected by its environment. Second order (in interaction strength, λ) master equations such as the Redfield equation are limited in their ability to describe reduced systems at long times, as they can only determine diagonal elements of the density matrix to order O(λ​​​​​​^​0). A fourth order master equation is necessary to determine all elements of the asymptotic state to the first nonzero order (λ²) precision. We establish a simplified form of the fourth order generator of the Non-Markovian time-convolutionless master equation (TCL4), which is then numerically implemented to efficiently find the steady state for an arbitrary finite system weakly coupled to a reservoir of linear oscillators at some finite temperature. With our optimal representation of the TCL4 generator, we investigate the requirements for return to equilibrium, and at zero temperature, approach to the global ground state. For systems such as the spin-boson model at zero temperature, where the Hamiltonian is known to not always admit a global ground state, we see that the TCL4 generator replicates this behavior, whereas the Redfield equation relaxes to a nonphysical ground state. We find that for the TCL4 master equation to have a convergent steady state, it must be asymptotically complete in the Hilbert Space.   

Effect of non-Markovian dephasing bath on Dicke phase transition

We study the zero temperature Dicke superradiant phase transition when each atom is coupled to an individual non-Markovian dephasing bath. By using tensor network methods, we find out that, in contrast to previous studies where the Markovian bath completely destroys the superradiant phase transition, non-Markovianity of the bath can restore the phase transition. We numerically extract the critical couplings associated with the superradiant phase transition.   

Giant atoms in a two-dimensional structured environment — protection from decoherence

Giant atoms are a new paradigm of quantum emitters that break the dipole approximation by coupling to light at multiple discrete points. Among their many promising properties, giant atoms have the ability to interact via a one-dimensional waveguide without decohering. Here, we study how giant atoms behave when coupled to a two-dimensional square lattice of coupled cavities. This particular environment has an energy spectrum characterized by finite bands and band gaps, which affect atomic dynamics beyond the Markovian regime. In this talk, we will show how giant atoms can avoid decoherence (through subradiance, decoherence-free interaction, and the overlap of bound states), and how their dynamics compare to that of small atoms and continuous waveguides. The results shown here may find applications in quantum simulation and quantum information processing.