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arXiv:1207.5768 · Physical Review A

Dissipative spin chains: Implementation with cold atoms and steady-state properties

Heike Schwager, J. I. Cirac, G. Giedke

Published Feb 13, 2013• 34 citations
arXivHTMLPDF

Abstract

We propose a quantum optical implementation of a class of dissipative spin systems, including the $XXZ$ and Ising model, with ultracold atoms in optical lattices. By employing the motional degree of freedom of the atoms and detuned Raman transitions, we show how to obtain engineerable dissipation and a tunable transversal magnetic field, enabling the study of the dynamics and steady-states of dissipative spin models. As an example of effects made accessible this way, we consider small spin chains and weak dissipation and show by numerical simulation that steady-state expectation values display pronounced peaks at certain critical system parameters. We show that this effect is related to degeneracies in the Hamiltonian and derive a sufficient condition for its occurrence.

DOI
10.1103/physreva.87.022110

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We propose a quantum optical implementation of a class of dissipative spin systems, including the XXZXXZXXZ and Ising model, with ultracold atoms in optical lattices. By employing the motional degree of freedom of the atoms and detuned Raman transitions, we show how to obtain engineerable dissipation and a tunable transversal magnetic field, enabling the study of the dynamics and steady-states of dissipative spin models. As an example of effects made accessible this way, we consider small spin chains and weak dissipation and show by numerical simulation that steady-state expectation values display pronounced peaks at certain critical system parameters. We show that this effect is related to degeneracies in the Hamiltonian and derive a sufficient condition for its occurrence.
We consider the nonequilibrium dynamics of a driven dissipative spin chain with chiral coupling to a one-dimensional (1D) bosonic bath, and its atomic implementation with a two-species mixture of cold quantum gases. The reservoir is represented by a spin-orbit coupled 1D quasicondensate of atoms in a magnetized phase, while the spins are identified with motional states of a separate species of atoms in an optical lattice. The chirality of reservoir excitations allows the spins to couple differently to left- and right-moving modes, which in our atomic setup can be tuned from bidirectional to purely unidirectional. Remarkably, this leads to a pure steady state in which pairs of neighboring spins form dimers that decouple from the remainder of the chain. Our results also apply to current experiments with two-level emitters coupled to photonic waveguides.
In this Thesis, we study open quantum spin systems from di↵erent perspectives.The first part is motivated by technological challenges of quantum computation.An important building block for quantum computation and quantum communication networks is an interface between material qubits for storage and data processing and travelling photonic qubits for communication.We propose the realisation of a quantum interface between a travelling-wave light field and the nuclear spins in a quantum dot strongly coupled to a cavity.Our scheme is robust against cavity decay as it uses the decay of the cavity to achieve the coupling between nuclear spins and the travelling-wave light fields.A prerequiste for such a quantum interface is a highly polarized ensemble of nuclear spins.High polarization of the nuclear spin ensemble is moreover highly desirable as it protects the potential electron spin qubit from decoherence.Here we present the theoretical description of an experiment in which highly asymmetric dynamic nuclear spin pumping is observed in a single self-assembled InGaAs quantum dot.The second part of this Thesis is devoted to fundamental studies of dissipative spin systems.We study general one-dimensional spin chains under dissipation and propose a scheme to realize a quantum spin system using ultracold atoms in an optical lattice in which both coherent interaction and dissipation can be engineered and controlled.This system enables the study of non-equilibrium and steady state physics of open and driven spin systems.We find, that the steady state expectation values of di↵erent spin models exhibit discontinuous behaviour at degeneracy points of the Hamiltonian in the limit of weak dissipation.This e↵ect can be used to dissipatively probe the spectrum of the Hamiltonian.We moreover study spin models under the aspect of state preparation and show that dissipation drives certain spin models into highly entangled state.Finally,
Using cold bosonic atoms with two (hyperfine) ground states, we introduce a spin-boson mixture that allows one to implement the quantum Ising model in a tunable dissipative environment. The first specie lies in a deep optical lattice with tightly confining wells and forms a spin array; spin-up (spin-down) corresponds to occupation by one (no) atom at each site. The second specie forms a superfluid reservoir. Different species are coupled coherently via laser transitions and collisions. Whereas the laser coupling mimics a transverse field for the spins, the coupling to the reservoir sound modes induces a ferromagnetic (Ising) coupling as well as dissipation. This gives rise to an order-disorder quantum phase transition where the effect of dissipation can be studied in a controllable manner.
A quantum many-body system coupled to an environment relaxes to a nonequilibrium steady state that can sustain order with no equilibrium counterpart. Computing such steady states is harder than closed-system dynamics as the density matrix problem squares the Hilbert-space dimension, and no free energy selects the steady state. The dissipative spin-1/2 Heisenberg chain is a benchmark example for nonequilibrium steady state physics; various methods have each calculated its phase diagram but do not agree, and a controlled determination at large system size has remained out of reach. Here we simulate the Lindblad dynamics of chains of up to 50 sites on the superconducting processor ibm_kingston -- 100 simultaneously active qubits at up to 1700 entangling-gate depths -- realizing the dissipation via Stinespring dilation. The system's dissipative evolution is a self-correcting mechanism that effectively erases errors, so hardware noise enters only as a weak competing dissipator. We measure static structure factors and resolve ferromagnetic, antiferromagnetic, spin-density-wave, and paramagnetic steady states, mapping the phase diagram with 117 quantum hardware data points across the JxJ_xJx​--JyJ_yJy​ plane. We uncover a rich non-equilibrium phase diagram of ordered phases with only remnants of the mean-field order, and where sharp transitions give way to the crossovers expected in one dimension. We also find the existence of an incipient (Trotter-induced) spin density wave phase, highlighting the potential of controlled Trotterization as a tool to engineer various magnetic phases in dissipative spin systems. Our quantum simulations largely settle the lingering uncertainty regarding the correct phase diagram of this benchmark system. Moreover, they show that quantum computers are now a feasible tool for addressing scientific questions involving dissipative quantum systems.
We study the dynamics of dissipative spin lattices with power-law interactions, realized via few-level atoms driven by coherent laser-coupling and decoherence processes. Using Monte Carlo simulations, we determine the phase diagram in the steady state and analyze its generation dynamics. As opposed to mean-field predictions and nearest-neighbor models, there is no transition to long-range-ordered phases for realistic interactions and resonant driving. However, for finite laser detunings, we demonstrate the emergence of crystalline order. Although the static and dynamical critical exponents of the revealed dissipative phase transition fall into the two-dimensional Ising universality class, the found steady states differ considerably from those of an equilibrium Ising magnet. Two complementary schemes for an experimental implementation with cold Rydberg atoms are discussed.
Open quantum many-body systems with controllable dissipation can exhibit novel features in their dynamics and steady states. A paradigmatic example is the dissipative transverse field Ising model. It has been shown recently that the steady state of this model with all-to-all interactions is genuinely non-equilibrium near criticality, exhibiting a modified time-reversal symmetry and violating the fluctuation-dissipation theorem. Experimental study of such non-equilibrium steady-state phase transitions is however lacking. Here we propose realistic experimental setups and measurement schemes for current trapped-ion quantum simulators to demonstrate this phase transition, where controllable dissipation is engineered via a continuous weak optical pumping laser. With extensive numerical calculations, we show that strong signatures of this dissipative phase transition and its non-equilibrium properties can be observed with a small system size across a wide range of system parameters. In addition, we show that the same signatures can also be seen if the dissipation is instead achieved via Floquet dynamics with periodic and probabilistic resetting of the spins. Dissipation engineered in this way may allow the simulation of more general types of driven-dissipative systems or facilitate the dissipative preparation of useful many-body entangled states.