Environmentally Induced Entanglement – Anomalous Behavior in the Adiabatic Regime

Abstract

Considering two non-interacting qubits in the context of open quantum systems, it is well known that their common environment may act as an entangling agent. In a perturbative regime the influence of the environment on the system dynamics can effectively be described by a unitary and a dissipative contribution. For the two-spin Boson model with (sub-) Ohmic spectral density considered here, the particular unitary contribution (Lamb shift) easily explains the buildup of entanglement between the two qubits. Furthermore it has been argued that in the adiabatic limit, adding the so-called counterterm to the microscopic model compensates the unitary influence of the environment and, thus, inhibits the generation of entanglement. Investigating this assertion is one of the main objectives of the work presented here. Using the hierarchy of pure states (HOPS) method to numerically calculate the exact reduced dynamics, we find and explain that the degree of inhibition crucially depends on the parameter s determining the low frequency power law behavior of the spectral density J(ω)∼ωse−ω/ωc. Remarkably, we find that for resonant qubits, even in the adiabatic regime (arbitrarily large ωc), the entanglement dynamics is still influenced by an environmentally induced Hamiltonian interaction. Further, we study the model in detail and present the exact entanglement dynamics for a wide range of coupling strengths, distinguish between resonant and detuned qubits, as well as Ohmic and deep sub-Ohmic environments. Notably, we find that in all cases the asymptotic entanglement does not vanish and conjecture a linear relation between the coupling strength and the asymptotic entanglement measured by means of concurrence. Further we discuss the suitability of various perturbative master equations for obtaining approximate entanglement dynamics.

Hamiltonian Model for Fault Tolerant Singlet-Like Excitation: First Principles Approach

“…At finite ω/ω c , there is incomplete cancellation of the terms, the effects of which have recently been studied in Ref. [25] Note that in our model, the renormalized system Hamiltonian is always block-diagonal. In the computational basis, it is…”

“…Without the counterterm, the Lambshift would cause the reduced system dynamics to significantly depend on ω c for ω c ∆, which is unphysical. Adding the counterterm cancels this linear dependence, [25] making the reduced system dynamics independent of ω c . This cancellation is studied in Sec.…”

“…[23,38,39] Even if the coupling is far below critical, the entanglement of the asymptotic state of the system, calculated using exact quantum dynamics, can differ significantly from that calculated by Markov master equations. [25] Since the phenomenon of FTES involves feedback from the bath, there is an immediate concern if the phenomenon is well represented by the Markov master equations. Thus, we will investigate if the phenomenon persists in non-Markovian dynamics.…”

“…[24] The efficiency of the method has recently been improved using quantum trajectory based hierarchy of stochastic pure states, [64][65][66] including investigation of entanglement between two spins mediated by the bath. [25] In this paper, we apply the time evolving matrix product operators (TEMPO) [21] technique. The main idea is to compress the ADT in the form of a matrix product state [67,68] using singular-value-decomposition (SVD), which can significantly extend the history time of the approximate path integral.…”

“…It is theoretically established that two qubits interacting solely via a common heat bath can exhibit permanent entanglement, depending on the system-bath coupling and bath parameters. [25,[73][74][75][76][77] The entanglement usually results from the unitary transformation that the heat bath applies on the qubit system. [19,31,32,[78][79][80] However, asymptotic entanglement of qubits is typically weak, as dissipative dynamics drives the system close to the ground state, which is not easily entangled.…”