Stochastic wave-function unraveling of the generalized Lindblad master equation

Moodley, Mervlyn; Petruccione, Francesco

doi:10.1103/physreva.79.042103

Cited by 35 publications

(71 citation statements)

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“…In fact, microscopic dynamics that lead to a given kernel are generally unknown. On the other hand, assuming that a continuous-in-time measurement process is performed over the system, it is not known which kind of stochastic trajectories [29][30][31][32][33] may describe the conditional system dynamics [22][23][24][25][26][27][28]. The main goal of this paper is to answer these issues.…”

Section: Introductionmentioning

confidence: 99%

“…Different theoretical approaches and physical situations had been analyzed by many authors in order to establish and characterize these equations [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. The unravelling of the non-Markovian dynamics in terms of measurement trajectories has also been extensively studied [22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

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Post-Markovian quantum master equations from classical environment fluctuations

Budini

2014

Phys. Rev. E

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In this paper we demonstrate that two commonly used phenomenological post-Markovian quantum master equations can be derived without using any perturbative approximation. A system coupled to an environment characterized by self-classical configurational fluctuations, the latter obeying a Markovian dynamics, defines the underlying physical model. (2010)], we also demonstrate that these master equations, even with exponential memory functions, may lead to non-Markovian effects such as an environment-to-system backflow of information if the Hamiltonian system does not commutate with the dissipative dynamics.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Post-Markovian quantum master equations from classical environment fluctuations

Budini

2014

Phys. Rev. E

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“…It turns out that the popular Markovian approximation which does not take into account memory effects is not sufficient for modern applications and todays technology calls for truly nonMarkovian approach. Non-Markovian dynamics was recently studied in [3][4][5][6][7][8][9][10][11][12][13][14][15]. Interestingly, several measures of non-Markovianity were proposed during last year [16][17][18][19].…”

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confidence: 99%

Non-Markovian Quantum Dynamics: Local versus Nonlocal

2010

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We analyze non-Markovian evolution of open quantum systems. It is shown that any dynamical map representing evolution of such a system may be described either by non-local master equation with memory kernel or equivalently by equation which is local in time. These two descriptions are complementary: if one is simple the other is quite involved, or even singular, and vice versa. The price one pays for the local approach is that the corresponding generator keeps the memory about the starting point 't0'. This is the very essence of non-Markovianity. Interestingly, this generator might be highly singular, nevertheless, the corresponding dynamics is perfectly regular. Remarkably, singularities of generator may lead to interesting physical phenomena like revival of coherence or sudden death and revival of entanglement. [2]. It turns out that the popular Markovian approximation which does not take into account memory effects is not sufficient for modern applications and todays technology calls for truly nonMarkovian approach. Non-Markovian dynamics was recently studied in [3][4][5][6][7][8][9][10][11][12][13][14][15]. Interestingly, several measures of non-Markovianity were proposed during last year [16][17][18][19].The standard approach to the dynamics of open system uses the Nakajima-Zwanzig projection operator technique [20] which shows that under fairly general conditions, the master equation for the reduced density matrix ρ(t) takes the form of the following non-local equationin which quantum memory effects are taken into account through the introduction of the memory kernel K(t): this simply means that the rate of change of the state ρ(t) at time t depends on its history (starting at t = t 0 ). Usually, one takes t 0 = 0, however, in this letter we shall keep 't 0 ' arbitrary. An alternative and technically much simpler scheme is the time-convolutionless (TCL) projection operator technique [1,21,22] in which one obtains a first-order differential equation for the reduced density matrix. The advantage of the TCL approach consists in the fact that it yields an equation of motion for the relevant degrees of freedom which is local in time and which is therefore often much easier to deal with than the Nakajima-Zwanzig non-local master equation (1).An essential step to derive TCL from (1) relies on the existence of certain operator inverse [22]. However, this inverse needs not exist and then the method does not work [1,22]. Moreover, even if it exists the corresponding local in time TCL generator is usually defined by the perturbation series (see e.g. detailed discussion in [1]) in powers of the coupling strength characterizing the system. However in general the perturbative approach leads to significant problems. For example the dynamical map needs not be completely positive if one takes only finite number of terms from the perturbative expansion.In the present paper we take a different path. We show that any solution of the non-local equation (1) always satisfies equation which does not involve the integral memory k...

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“…Again, we expect this to improve the SNR by ∼ √ 2. For computational efficiency in our Monte-Carlo simulations, we unravel the master equation to produce a stochastic Schrodinger equation [22,25], including four stochastic processes: three quantum diffusion processes, one each for the cavity fields and an additional process to account for cross relaxation of the transmon into the waveguide, and one quantum-jump process for the signal photon pulse. 2 In the absence of a signal photon, the evolution of the unnormalized 1 The subscript denotes a single cavity-transmon unit.…”

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confidence: 99%

Non-absorbing high-efficiency counter for itinerant microwave photons

Fan

Milburn

Stace

2014

Research in Optical Sciences

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Detecting an itinerant microwave photon with high efficiency is an outstanding problem in microwave photonics and its applications. We present a scheme to detect an itinerant microwave photon in a transmission line via the nonlinearity provided by a transmon in a driven microwave resonator. With a single transmon we achieve 84% distinguishability between zero and one microwave photons and 90% distinguishability with two cascaded transmons by performing continuous measurements on the output field of the resonator. We also show how the measurement diminishes coherence in the photon number basis thereby illustrating a fundamental principle of quantum measurement: The decoherence rate increases as the detector is made more effective. Conventional photon detectors, such as avalanche photodiode (APD) and photomultiplier tube (PMT), are widely used in practice. However, they destroy the signal photon during detection. There are a number of schemes for quantum nondemolition (QND) optical photon detection [3][4][5], but typically they require a high-Q cavity for storing the signal mode containing the photon(s) to be detected, and a leaky cavity for manipulating and detecting the probe mode. Thus, during one lifetime of a signal photon, the probe mode undergoes many cycles to accumulate information about the signal. This type of detection requires repeated measurements, and the high-Q cavity limits the photodetection bandwidth. In the microwave regime the detection of single photons [6][7][8][9][10][11][12][13][14][15] is more challenging, especially nondestructive detection [6,9,14,15]. Here we propose a scheme for nonabsorbing, high-efficiency detection of single itinerant microwave photons via the nonlinearity provided by an artificial superconducting atom, a transmon [16].Previously [15,17], we considered schemes where the signal photon wave packet propagates freely in an open transmission line [11,18] and encounters the lowest transition of a transmon. The cw-probe field couples the first and second excited states of the transmon and is monitored via continuous homodyne detection. Displacements in the homodyne current, due to the large transmon-induced cross-Kerr nonlinearity [18], indicate the presence of a photon. We showed that, in spite of the exceptionally large cross-Kerr nonlinearity it exhibits [18], a single transmon in an open transmission line is insufficient for reliable microwave photon detection, due to saturation of the transmon response to the probe field [17]. More recently [15], we showed that multiple cascaded transmons could achieve reliable microwave photon counting in principle, though the number of transmons and circulators required in this scheme presents serious experimental challenges.In this paper we propose a scheme that achieves reliable photon counting with as few as a single transmon. The key * stace@physics.uq.edu.au insight is to use a cavity resonant with the probe field to enhance the probe displacements, which depends on the signal photon number. We quantify the measurement efficie...

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Stochastic wave-function unraveling of the generalized Lindblad master equation

Cited by 35 publications

References 31 publications

Post-Markovian quantum master equations from classical environment fluctuations

Post-Markovian quantum master equations from classical environment fluctuations

Non-Markovian Quantum Dynamics: Local versus Nonlocal

Non-absorbing high-efficiency counter for itinerant microwave photons

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