Quantum trajectories for realistic photodetection: II. Application and analysis

Warszawski, Prahlad; Wiseman, Howard Mark

doi:10.1088/1464-4266/5/1/302

Cited by 26 publications

(25 citation statements)

References 19 publications

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“…Now we employ the convection equation (28) in order to eliminate z t , ẇ( ), and we substitute the solution (29) into the expression for the classical noise (36):…”

Section: Dressed Non-markovian Quantum Trajectorymentioning

confidence: 99%

“…In the Markovian regime, when the environment recovers instantly after the OQS disturbances, it is fairly well understood how to characterize and propagate the state of an open system: its state is represented either by a reduced density matrix, which is governed by a master equation [23]; or by a wavefunction, which is governed by a stochastic Schrodinger equation [23][24][25][26][27][28][29][30][31][32][33]. Closely related to these methods is the input-output formalism [34][35][36], which allows one to take into account the properties of the incident and scattered excitations of the bath.…”

Section: Introductionmentioning

confidence: 99%

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Dressed quantum trajectories: novel approach to the non-Markovian dynamics of open quantum systems on a wide time scale

Polyakov

Rubtsov

2019

New J. Phys.

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A new approach to theory and simulation of the non-Markovian dynamics of open quantum systems is presented. It is based on identification of a parameter which is uniformly bounded on wide time intervals: the occupation of the virtual cloud of quanta. By 'virtual' we denote those bath excitations which were emitted by the open system, but eventually will be reabsorbed before any measurement of the bath state. A useful property of the virtual cloud is that the number of its quanta is expected to saturate on long times, since physically this cloud is a (retarded) polarization of the bath around the system. Therefore, the joint state of open system and virtual cloud (we call it dressed state) can be accurately represented in a truncated basis of Fock states, on a wide time scale. At the same time, there can be an arbitrarily large number of the observable quanta (which survive up to measurement), especially if the open system is under driving. However, it turns out that the statistics of the bathmeasurement outcomes is classical (in a suitable measurement basis): one can employ a Monte Carlo sampling of these outcomes. Therefore, it is possible to efficiently simulate the dynamics of the observable quantum field. In this work we consider the bath measurement with respect to the coherent states, which yields the Husimi function as the positive (quasi)probability distribution of the outcomes. The joint evolution of the dressed state and the corresponding outcome is called the dressed quantum trajectory. The Monte Carlo sampling of these trajectories yields a stochastic simulation method with promising convergence properties on wide time scales.

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“…Now we employ the convection equation (28) in order to eliminate z t , ẇ( ), and we substitute the solution (29) into the expression for the classical noise (36):…”

Section: Dressed Non-markovian Quantum Trajectorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dressed quantum trajectories: novel approach to the non-Markovian dynamics of open quantum systems on a wide time scale

Polyakov

Rubtsov

2019

New J. Phys.

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“…This is possible using the simulation technique of Ref. [10], in which the realistic quantum trajectory can be assured to be consistent with the ideal quantum trajectory.…”

Section: Conditional Probability Distribution For Driving Strengthmentioning

confidence: 99%

“…To treat realistic detection we use the theory developed in Refs. [8][9][10]. This generalized the theory of quantum trajectories [11][12][13][14][15][16] by determining the state of the system conditioned upon the output of a detector that has dead time ͑ dd ͒, dark counts at rate ␥ dk , inefficiency , and finite bandwidth ␥ r .…”

Section: Introductionmentioning

confidence: 99%

Dynamical parameter estimation using realistic photodetection

2004

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We investigate the effect of imperfections in realistic detectors upon the problem of quantum state and parameter estimation by continuous monitoring of an open quantum system. Specifically, we have reexamined the system of a two-level atom with an unknown Rabi frequency introduced by Gambetta and Wiseman [Phys. Rev. A 64, 042105 (2001)]. We consider only direct photodetection and use the realistic quantum trajectory theory reported by Warszawski, Wiseman, and Mabuchi [Phys. Rev. A 65, 023802 (2002)]. The most significant effect comes from a finite bandwidth, corresponding to an uncertainty in the response time of the photodiode. Unless the bandwidth is significantly greater than the Rabi frequency, the observer's ability to obtain information about the unknown Rabi frequency, and about the state of the atom, is severely compromised. This result has implications for quantum control in the presence of unknown parameters for realistic detectors, and even for ideal detectors, as it implies that most of the information in the measurement record is contained in the precise timing of the detections.Comment: 8 pages, 6 figure

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“…7. It is possible to do this, following the method introduced for photodetectors in Refs.. 14,15 The result is a stochastic Fokker-Planck equation for ρ c (Q), where Tr[ρ c (Q) is the conditional probability that the charge on the capacitor is Q, and where dQρ c (Q) is the conditional quantum state, averaged over the unobserved charge Q. The details of this equation, and its derivation, will be left to a future publication.…”

Section: Non-ideal Qpc Casementioning

confidence: 99%

Noise in detection of qubit states using a quantum point contact

2003

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We present a model for detection of the states of a coupled quantum dots (qubit) by a quantum point contact. Most proposals for measurements of states of quantum systems are idealized. However in a real laboratory the measurements cannot be perfect due to practical devices and circuits. The models using ideal devices are not sufficient for describing the detection information of the states of the quantum systems. Our model therefore includes the extension to a non-ideal measurement device case using an equivalent circuit. We derive a quantum trajectory that describes the stochastic evolution of the state of the system of the qubit and the measuring device. We calculate the noise power spectrum of tunnelling events in an ideal and a non-ideal quantum point contact measurement respectively. We found that, for the strong coupling case it is difficult to obtain information of the quantum processes in the qubit by measurements using a non-ideal quantum point contact. The noise spectra can also be used to estimate the limits of applicability of the ideal model.

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Quantum trajectories for realistic photodetection: II. Application and analysis

Cited by 26 publications

References 19 publications

Dressed quantum trajectories: novel approach to the non-Markovian dynamics of open quantum systems on a wide time scale

Dressed quantum trajectories: novel approach to the non-Markovian dynamics of open quantum systems on a wide time scale

Dynamical parameter estimation using realistic photodetection

Noise in detection of qubit states using a quantum point contact

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