Conservation law of operator current in open quantum systems

Salmilehto, Juha; Solinas, Paolo; Möttönen, Mikko

doi:10.1103/physreva.85.032110

Cited by 29 publications

(43 citation statements)

References 19 publications

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“…However, no detailed study on the effect of RWA and SA on non-Markovian behavior exists. Is non-Markovianity in general as vulnerable to SA as the conservation of electric charge in the Cooper pair pump [31][32][33]?…”

Section: Introductionmentioning

confidence: 99%

Effects of the rotating-wave and secular approximations on non-Markovianity

Mäkelä

Möttönen

2013

Phys. Rev. A

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We study the effect of the rotating-wave approximation (RWA) and the secular approximation (SA) on the non-Markovian behavior in the spin-boson model at zero-temperature. We find that both the RWA and SA lead to a dramatic reduction in the observed non-Markovianity. In general, nonMarkovian dynamics is observed for the whole relaxation time of the system, whereas the RWA and SA lead to such dynamics only on the short time scale of the environmental correlation time. Thus, the RWA and SA are not necessarily justified in the studies of non-Markovianity although they can estimate the state of the system precisely. Furthermore, we derive an accurate analytical expression for the non-Markovianity measure without the RWA or SA. This expression yields important insight into the physics of the problem.

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Section: Introductionmentioning

confidence: 99%

Effects of the rotating-wave and secular approximations on non-Markovianity

Mäkelä

Möttönen

2013

Phys. Rev. A

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“…The distortion reflects the breakdown of the secular approximation -often made in derivations -because the capacitive coupling λ can be of the same order as the internal qubit splitting Ω. Importantly, the distortion must be included to satisfy an isospin sum rule that follows from the conservation of the isospin by the tunneling of sensor electrons [32,46]. The distortion is thus enforced by a general principle.…”

Section: Discussionmentioning

confidence: 99%

“…The latter derives from the conservation of the total isospin, τ = τ 0 + τ 1 , when electrons tunnel from the electrodes into the SQD and vice versa, a generic feature [46] of indirect measurement models of type (1). We next discuss the expressions and physical significance of the four new coefficients γ 0 , γ 1 , c, and κ occurring in Eq.…”

Section: Kinetic Equationmentioning

confidence: 99%

“…[46] and [32], in particular, see Appendices D and E. Equation (18) shows that the reduction of the purity of the qubit state appears only due to noncollinearities of τ 0 and τ 1 . These noncollinearities develop because of the readout: the isospins τ 0 and τ 1 are subject to different effective "magnetic" fields depending on the charge state n of the sensor QD.…”

Section: B Weak-measurement and Weak-tunneling Limitmentioning

confidence: 99%

“…One way to eliminate the initial slip is to switch off the capacitive interaction before t = 0, i.e., λ(t) = 0 for −1/γ ≪ t < 0. Then the detector can establish a stationary state and the initial SQD-qubit state factorizes: (46] and see also Appendix C). By contrast, if one switches off the current through the sensor, Γ → 0, before t = 0, then one starts with a sensor in a definite charge state p 1 (0) = 0 or 1, which is highly nonstationary for typical operation parameters of the SQD (tuned close to resonance for high sensitivity, one finds usually p 0 st ∼ p 1 st ).…”

Section: E Effective Evolution Of Quasistationary Modesmentioning

confidence: 99%

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Qubit quantum-dot sensors: Noise cancellation by coherent backaction, initial slips, and elliptical precession

2016

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We theoretically investigate the backaction of a sensor quantum dot with strong local Coulomb repulsion on the transient dynamics of a qubit that is probed capacitively. We show that the measurement backaction induced by the noise of electron cotunneling through the sensor is surprisingly mitigated by the recently identified coherent backaction [M. Hell, M. R. Wegewijs, and D. P. DiVincenzo, Phys. Rev. B 89, 195405 (2014)] arising from quantum fluctuations. This indicates that a sensor with quantized states may be switched off better than naively expected. This renormalization effect is missing in semiclassical stochastic fluctuator models and typically also in Born-Markov approaches, which try to avoid the calculation of the nonstationary, nonequilibrium state of the qubit plus sensor. Technically, we integrate out the current-carrying electrodes to obtain kinetic equations for the joint, nonequilibrium detector-qubit dynamics. We show that the sensor current response, level renormalization, cotunneling broadening, and leading non-Markovian corrections always appear together and cannot be turned off individually in an experiment or ignored theoretically. We analyze the backaction on the reduced qubit state -capturing the full non-Markovian effects imposed by the sensor quantum dot on the qubit -by applying a Liouville-space decomposition into quasistationary and rapidly decaying modes. Importantly, the sensor cannot be eliminated completely even in the simplest high-temperature, weak-measurement limit since the qubit state experiences an initial slip depending on the initial preparation of qubit plus sensor quantum dot. The slip persists over many qubit cycles, i.e., also on the time scale of the qubit decoherence induced by the backaction. A quantum-dot sensor can thus not be modeled as usual as a "black box" without accounting for its dynamical variables; it is part of the quantum circuit. We furthermore find that the Bloch vector relaxes (rate 1/T1) along an axis that is not orthogonal to the plane in which the Bloch vector dephases (rate 1/T2), blurring the notions of relaxation and dephasing times. Moreover, the precessional motion of the Bloch vector is distorted into an ellipse in the tilted dephasing plane.

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The features of a quantum description of radiation in an optically dense medium

2015

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This paper is devoted to the theory of quantum electromagnetic field in an optically dense medium. Self-consistent equations describing interaction between a quantum field and a quantum dielectric medium are obtained from the first principles, i.e., outside a phenomenological description. Using these equations, we found a transformation (of the Bogoliubov transformation type) that converts the operators of the "vacuum" field into operators of collective perturbations of the field and an ensemble of atoms, that is, photons in the medium. Transformation parameter is the refractive index of the wave mode considered. It is shown that besides the energy of the collective electromagnetic field, the energy of photons in the medium includes the energy of the internal degrees of freedom of the substance and the energy of near-field dipole interaction between atoms in the polarized medium. The concept of negative energy photons is introduced on the basis of self-consistent equations.Keywords: Optically dense medium, quantum field, Bogoliubov transformation, photons in the medium 2 cuum). For example, for the medium with polarizability  and refractive index     4 1 2 2    n ck the result obtained within this approach corresponds to the approximation of small optical density, 12 n  . Despite the obvious constraints, this approach can be very effective. The point is that the approximation of small optical depth, i.e., the assumption that 11 n   in a fairly narrow frequency band, does not contradict, in principle, the condition of strong frequency dispersion, 1     n . As an example, we mention the effect of electromagnetically induced transparency (EIT) [24][25][26][27]: which suggests that within the "transparency window" there is a frequency range in which a small group velocity is combined with an almost "vacuum" phase velocity. However, in general (including some of the EIT modes, see [26,27]), the constraint 11 n   is awkward. To our knowledge, the analysis which is free of both the constraints of the phenomenological approach and the small optical density approximation, was carried out only in terms of a two-level model [5,[28][29][30].This paper is devoted to the development of the theory of quantum field in a medium with an arbitrary optical density and an arbitrary energy-level structure. Selecting as the initial model an ensemble of atoms interacting through a collective field, we came to fairly universal operator equations of quantum electrodynamics of a dielectric medium without spatial dispersion. Using these equations, it was found that the exact dispersion relation   k    for photons in the medium corresponds to the quanta of collective excitations of the field and the medium, and the energy   k   of a quantum includes the energy of the macroscopic field, the energy of the internal degrees of freedom, and the energy of the near-field dipole interaction in the polarized medium. It is shown that the operators of creation and annihilation the photon in the medium are related with t...

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Conservation law of operator current in open quantum systems

Cited by 29 publications

References 19 publications

Effects of the rotating-wave and secular approximations on non-Markovianity

Effects of the rotating-wave and secular approximations on non-Markovianity

Qubit quantum-dot sensors: Noise cancellation by coherent backaction, initial slips, and elliptical precession

The features of a quantum description of radiation in an optically dense medium

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