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arXiv:2005.08023 · Physical review. B./Physical review. B

Balancing coherent and dissipative dynamics in a central-spin system

Alessandro Ricottone, Yinan Fang, W. A. Coish

Published Aug 10, 2020• 7 citations
arXivHTMLPDF

Abstract

The average time required for an open quantum system to reach a steady state (the steady-state time) is generally determined through a competition of coherent and incoherent (dissipative) dynamics. Here, we study this competition for a ubiquitous central-spin system, corresponding to a central-spin-1/2 coherently coupled to ancilla spins and undergoing dissipative spin relaxation. The ancilla system can describe $N$ spins-1/2 or, equivalently, a single large spin of length $I=N/2$. We find exact analytical expressions for the steady-state time in terms of the dissipation rate, resulting in a minimal (optimal) steady-state time at an optimal value of the dissipation rate, according to a universal curve. Due to a collective-enhancement effect, the optimized steady-state time grows only logarithmically with increasing $N=2I$, demonstrating that the system size can be grown substantially with only a moderate cost in steady-state time. This paper has direct applications to the rapid initialization of spin qubits in quantum dots or bound to donor impurities, to dynamic nuclear-spin polarization protocols, and may provide key intuition for the benefits of error-correction protocols in quantum annealing.

DOI
10.1103/physrevb.102.085413

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The average time required for an open quantum system to reach a steady state (the steady-state time) is generally determined through a competition of coherent and incoherent (dissipative) dynamics. Here, we study this competition for a ubiquitous central-spin system, corresponding to a central-spin-1/2 coherently coupled to ancilla spins and undergoing dissipative spin relaxation. The ancilla system can describe NNN spins-1/2 or, equivalently, a single large spin of length I=N/2I=N/2I=N/2. We find exact analytical expressions for the steady-state time in terms of the dissipation rate, resulting in a minimal (optimal) steady-state time at an optimal value of the dissipation rate, according to a universal curve. Due to a collective-enhancement effect, the optimized steady-state time grows only logarithmically with increasing N=2IN=2IN=2I, demonstrating that the system size can be grown substantially with only a moderate cost in steady-state time. This paper has direct applications to the rapid initialization of spin qubits in quantum dots or bound to donor impurities, to dynamic nuclear-spin polarization protocols, and may provide key intuition for the benefits of error-correction protocols in quantum annealing.
We investigate dissipative phase transitions in an open central spin system. In our model the central spin interacts coherently with the surrounding many-particle spin environment and is subject to coherent driving and dissipation. We develop analytical tools based on a self-consistent Holstein-Primakoff approximation that enable us to determine the complete phase diagram associated with the steady states of this system. It includes first- and second-order phase transitions, as well as regions of bistability, spin squeezing, and altered spin-pumping dynamics. Prospects of observing these phenomena in systems such as electron spins in quantum dots or nitrogen-vacancy centers coupled to lattice nuclear spins are briefly discussed.
Abstract We study the dynamics of a qubit system interacting with thermalized bath-ancilla spins via a repeated interaction scheme. Considering generic initial conditions for the system and employing a Heisenberg-type interaction between the system and the ancillas, we analytically prove the following: (i) the populations and coherences of the qubit system evolve independently toward a nonequilibrium steady-state solution, which is diagonal in the qubit’s energy eigenbasis. The population relaxes to this state geometrically, whereas the coherences decay through a more compound behavior. (ii) In the long time limit, the system approaches a steady state that generally differs from the thermal state of the ancilla. We derive this steady-state solution and show its dependence on the interaction parameters and collision frequency. (iii) We bound the number of interaction steps required to achieve the steady state within a specified error tolerance, and we evaluate the energetic cost associated with the process. Our key finding is that deterministic system-ancilla interactions do not typically result in the system thermalizing to the thermal state of the ancilla. Instead, they generate a distinct nonequilibrium steady state, which we explicitly derive. However, we also identify an operational regime that leads to thermalization with a few long and possibly randomized collisions.
Abstract Understanding thermalization and irreversibility in open quantum systems requires char-acterizing the competition between coherent unitary dynamics and dissipative environmen-tal interactions. In this work, we present a systematic numerical study of thermalization dynamics in a two-qubit open quantum system governed by a completely positive and trace-preserving Lindblad master equation. The coherent evolution rate is controlled by a real scaling parameter α multiplying the Hamiltonian commutator, while decoherence is indepen-dently controlled by a dephasing rate γ . Although such a scaling of coherent dynamics can be absorbed into a rescaling of time in isolated systems, it becomes physically meaningful in open systems where decoherence introduces an absolute timescale. We investigate how the relative strength of coherent evolution and decoherence influences observable dynamics, purity decay, entropy production, and thermalization times. Using robust local and two-site observables, we show that varying α at fixed γ produces distinct transient trajectories, even though all evolutions converge to the same steady state. We further define an operational thermalization time τ ( γ, α ) based on a purity threshold and map the resulting thermalization-time surface across a broad parameter range. Increasing α generally accelerates oscillatory dynamics and modifies the approach to equilibrium, leading to measurable shifts in thermalization times without altering asymptotic states. These findings provide a clear and physically consistent characterization of how Hamil-tonian strength and decoherence rate jointly determine thermalization behavior in open quantum systems. The framework offers a practical parameterization for numerical mod-eling and experimental studies of coherent–dissipative competition in quantum information processing, quantum control, and open-system dynamics.
Entanglement underpins the power of quantum technologies, yet it is fragile and typically destroyed by dissipation. Paradoxically, the same dissipation, when carefully engineered, can drive a system toward robust entangled steady states. However, this engineering task is nontrivial, as dissipative many-body systems are complex, particularly when they support multiple steady states. Here, we derive analytic expressions that predict how the steady state of a system evolving under a Lindblad equation depends on the initial state, without requiring integration of the dynamics. These results extend Refs. [V. V. Albert and L. Jiang, ; V. V. Albert , ], showing that while the steady-state manifold is determined by the Liouvillian kernel, the weights within it depend on both the Liouvillian and the initial state. We identify a special class of Liouvillians for which the steady state depends only on the initial overlap with the kernel. Our framework provides analytical insight and a computationally efficient tool for predicting steady states in open quantum systems. As an application, we propose schemes to generate metrologically useful entangled steady states in spin ensembles via balanced collective decay.
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.
Understanding quantum coherence and proposing protection mechanisms has become one of the fundamental challenges in quantum physics research. We investigate a generic driven open quantum system, i.e., the driven spin-boson model, beyond the rotating-wave approximation. Although steady-state coherence vanishes in Floquet-Markov and Bloch-Redfield approaches, it becomes finite within a time-non-local master equation with a memory kernel. We analytically reveal that the steady-state coherence is associated with the overlap between the spectral densities associated with neighboring Floquet quasifrequencies. Motivated by this, we show that increasing temperature and introducing mixed transverse and longitudinal baths broadens the spectral density, thereby enhancing steady-state coherence. This is described by resonance fluorescence spectra, which exhibit clear spectral broadening and enhanced steady-state values. For a transverse dissipative coupling to the bath, three transition frequencies emerge in the Floquet basis, corresponding to the Mollow triplet. For weak resonant driving, these quasienergies become nearly degenerate, leading to closely spaced peaks in the resonance fluorescence spectrum, and the steady-state quantum coherence asymptotically approaches its maximum. For a longitudinal coupling to the bath, the quantum system exhibits a single transition frequency, thereby resulting in a complete suppression of the steady-state quantum coherence. We systematically investigate the influences of driving strength, frequency, temperature, and various dissipative baths on steady-state quantum coherence. These findings provide a foundational framework for efficiently engineering steady-state quantum coherence in nanoscale open quantum devices under optical field excitation.