Exact non-Markovian master equation for a driven damped two-level system

Shen, H. Z.; Qin, M.; Xiu, Xiao‐Ming

doi:10.1103/physreva.89.062113

Cited by 28 publications

(22 citation statements)

References 78 publications

(150 reference statements)

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“…(4), it allows us to factor out contractions of C † k (t)-entering from the adjoint of Eq. (11)-and D j (t); specifically, we find (17) for any A(t) that satisfies Eq. (16).…”

mentioning

confidence: 89%

“…Having appeared first in [18], it reappears in a recent work of Shen et al [17], along with a derivation from Feynman-Vernon influence functional theory which invokes a coherent state representation in Grassmannian variables for the qubit state. We show in this paper that the derived time-local master equation is incorrect; it is not influence functional theory and coherent-state path integrals that yield a successful derivation, but linearity, which for the driven qubit is lost.…”

mentioning

confidence: 99%

“…We emphasize, however, that the simple extrapolation holds only when the driving is weak. Shen et al [17] report a derivation with no such restriction; they assume a zero-temperature environment but admit coherent driving of any strength. They return to the equation from [18] and revive Cresser's concern [11]: "Such a relatively simple result .…”

mentioning

confidence: 99%

“…It is only met for zero drive; otherwise the equation derived in Ref. [17], where −i [ξ(t)σ + + ξ * (t)σ − , ρ S (t)] is added to the right-hand side of Eq. (26), is incorrect.…”

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confidence: 99%

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Time-local Heisenberg-Langevin equations and the driven qubit

Whalen

Carmichael

2016

Phys. Rev. A

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The time-local master equation for a driven boson system interacting with a boson environment is derived by way of a time-local Heisenberg-Langevin equation. Extension to the driven qubit fails-except for weak excitation-due to the lost linearity of the system-environment interaction. We show that a reported time-local master equation for the driven qubit is incorrect. As a corollary to our demonstration, we also uncover odd asymptotic behavior in the "repackaged" time-local dynamics of a system driven to a far-from-equilibrium steady state: the density operator becomes steady while time-dependent coefficients oscillate (with periodic singularities) forever. Issues of formal exactness aside, the current move from given quantum systems-an atom or radiation field in a cavity-to engineered systems, drives a more pragmatic interest in the theory of non-Markovian open quantum systems. While generalizations of input-output theory to the non-Markovian regime have been considered [5][6][7], more commonly the Schrödinger picture is adopted, where, after the work of Hu et al. Treatments in the[8], time-local master equations are derived [9][10][11][12][13][14][15][16]. Of particular interest in this paper are the time-local master equation for a driven boson system in interaction with a boson environment (first derived in [11]) and the equation for spontaneous emission from a two-state system, or qubit [9][10][11][12]. They invite a conflation: a time-local master equation for the driven qubit.The driven qubit is an important example, considering its role in quantum information science and the numerous physical realizations. The question of a time-local master equation is an old one. It is raised in Sec. IVA of Ref. [11], where, after first noting obstacles to its derivation, the author mentions an equation reported in a preprint [18], following with: "Such a relatively simple result seems to be inconsistent with the conclusion reached above about the difficulty of dealing with the two level atom problem, and is hence an issue that requires further consideration." The noted equation is absent from the published version of [18] (Ref. [10]), which can be seen to endorse the call for "further consideration."The "relatively simple result" substitutes qubit raising and lowering operators for the creation and annihilation operators in the time-local master equation for the driven boson system. Having appeared first in [18], it reappears in a recent work of Shen et al. [17], along with a derivation from Feynman-Vernon influence functional theory which invokes a coherent state representation in Grassmannian variables for the qubit state. We show in this paper that the derived time-local master equation is incorrect; it is not influence functional theory and coherent-state path integrals that yield a successful derivation, but linearity, which for the driven qubit is lost. While in spontaneous emission [9][10][11][12] linearity is effectively retained-due to the one-quantum truncation-for the driven qubit, multiphoton scattering (...

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“…(4), it allows us to factor out contractions of C † k (t)-entering from the adjoint of Eq. (11)-and D j (t); specifically, we find (17) for any A(t) that satisfies Eq. (16).…”

mentioning

confidence: 89%

mentioning

confidence: 99%

mentioning

confidence: 99%

“…It is only met for zero drive; otherwise the equation derived in Ref. [17], where −i [ξ(t)σ + + ξ * (t)σ − , ρ S (t)] is added to the right-hand side of Eq. (26), is incorrect.…”

mentioning

confidence: 99%

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Time-local Heisenberg-Langevin equations and the driven qubit

Whalen

Carmichael

2016

Phys. Rev. A

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“…Recently, however, a number of investigations by incorporating Grassmann variables in fermionic systems have appeared in the literature [59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76]. Among them are the phase space methods for degenerate Fermi gases [59], counting statistics and quantum Monte-Carlo methods of strongly correlated fermions [62], superfluidity [67] and Cooper-like pairing in trapped fermions [68], to name just a few.…”

Section: Properties Of Anti-commuting Numbersmentioning

confidence: 99%

Born-Kothari Condensation for Fermions

Ghosh

2017

Entropy

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Abstract:In the spirit of Bose-Einstein condensation, we present a detailed account of the statistical description of the condensation phenomena for a Fermi-Dirac gas following the works of Born and Kothari. For bosons, while the condensed phase below a certain critical temperature, permits macroscopic occupation at the lowest energy single particle state, for fermions, due to Pauli exclusion principle, the condensed phase occurs only in the form of a single occupancy dense modes at the highest energy state. In spite of these rudimentary differences, our recent findings [Ghosh and Ray, 2017] identify the foregoing phenomenon as condensation-like coherence among fermions in an analogous way to Bose-Einstein condensate which is collectively described by a coherent matter wave. To reach the above conclusion, we employ the close relationship between the statistical methods of bosonic and fermionic fields pioneered by Cahill and Glauber. In addition to our previous results, we described in this mini-review that the highest momentum (energy) for individual fermions, prerequisite for the condensation process, can be specified in terms of the natural length and energy scales of the problem. The existence of such condensed phases, which are of obvious significance in the context of elementary particles, have also been scrutinized.

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