Quantum dynamics intervened by repeated nonselective measurements (original) (raw)
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Continual measurements for quantum open systems
Il Nuovo Cimento B Series 11, 1983
Starting from the recently introduced formalism of continual measurements in quantum mechanics, it is shown that, for the quantum open systems, it is possible to construct probability distributions for the values at all times of certain observables, without the continual measurement of such observables perturbing the dynamics of the system. )/[ore precisely, starting from the quantum description of an open system, a generalized stochastic process for certain observables is constructed, which is independent of the fact that these observables are actually measured or not. The example of the quantum Brownian motion is developed in detail. In such an example it is shown how the a priori arbitrary elements of the formalism are in reality determined by the dynamics of the system. PACS. 03.65. -Quantum theory; quantum mechanics. PACS. 02.50. -Probability theory, stochastic processes and statistics. PACS. 05.40. -Fluctuation phenomena, random processes and Brownian motion.
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Quantum open systems are described in the Markovian limit by master equations in Lindblad form. I argue that common "quantum trajectory" techniques corresponding to continuous measurement schemes, which solve the master equation by unraveling its evolution into stochastic trajectories in Hilbert space, correspond closely to particular sets of decoherent (or consistent) histories. This is illustrated by a simple model of photon counting. An equivalence is shown for these models between standard quantum jumps and the orthogonal jumps of Diósi, which have already been shown to correspond to decoherent histories. This correspondence is compared to simple treatments of trajectories based on repeated or continuous measurements.
Quantum evolution in the stroboscopic limit of repeated measurements
We consider a quantum system dynamics caused by successive selective and non-selective measurements of the probe coupled to the system. For the finite measurement rate τ −1 and the system-probe interaction strength γ we derive analytical evolution equations in the stroboscopic limit τ → 0 and γ 2 τ = const, which can be considered as a deviation from the Zeno subspace dynamics on a longer timescale T ∼ (γ 2 τ) −1 γ −1. Non-linear quantum dynamics is analyzed for selective stroboscopic projective measurements of an arbitrary rank. Non-selective measurements are shown to induce the semigroup dynamics of the system-probe aggregate. Both non-linear and decoherent effects become significant at the timescale T ∼ (γ 2 τ) −1 , which is illustrated by a number of examples.
Quantum measurements in continuous time, non-Markovian evolutions and feedback
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012
In this article we reconsider a version of quantum trajectory theory based on the stochastic Schrödinger equation with stochastic coefficients, which was mathematically introduced in the '90s, and we develop it in order to describe the non Markovian evolution of a quantum system continuously measured and controlled thanks to a measurement based feedback. Indeed, realistic descriptions of a feedback loop have to include delay and thus need a non Markovian theory. The theory allows to put together non Markovian evolutions and measurements in continuous time in agreement with the modern axiomatic formulation of quantum mechanics. To illustrate the possibilities of such a theory, we apply it to a two-level atom stimulated by a laser. We introduce closed loop control too, via the stimulating laser, with the aim to enhance the "squeezing" of the emitted light, or other typical quantum properties. Note that here we change the point of view with respect to the usual applications of control theory. In our model the "system" is the two-level atom, but we do not want to control its state, to bring the atom to a final target state. Our aim is to control the "Mandel Q-parameter" and the spectrum of the emitted light; in particular the spectrum is not a property at a single time, but involves a long interval of times (a Fourier transform of the autocorrelation function of the observed output is needed).
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Nonclassical dynamics induced by a quantum meter
Physical Review A, 2005
Conventionally, the effect of measurements on a quantum system is assumed to introduce decoherence, which renders the system classical-like. We consider here a microscopic meter, that is, an auxiliary essentially quantum system whose state is measured repeatedly, and show that it can be employed to induce transitions from classical states into inherently quantumlike states. The meter state is assumed to be lost in the environment and we derive a non-Markovian master equation for the dynamic system in the case of nondemolition coupling to the meter; this equation can be cast in the form of an ͑N a ͒th-order differential equation in time, where N a is the dimension of the meter basis. We apply the approach to a harmonic oscillator coupled to a spin-1 2 meter and demonstrate how it can be used to engineer effective Hamiltonian evolution, subject to decoherence induced by the projective meter measurements.
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Physica Scripta, 2015
The inhibition of the decay of a quantum system by frequent measurements is known as quantum Zeno effect. Beyond the limit of projective measurements, the interplay between the unitary dynamics of the system and the coupling to a measurement apparatus becomes relevant. We explore this interplay by considering a quantum particle moving on a one-dimensional chain. A local measurement by coupling to an apparatus with a two-dimensional Hilbert space detects the presence of the particle on a specific chain site. The decay of the population is studied analytically for a two-site chain and numerically for a larger system as a function of the measurement time and the time between subsequent measurements. Particular attention is given to the shift of the energy of the measured site due to the coupling to the apparatus. The decay of the initial population can be hindered or accelerated, depending on the chosen system and the coupling parameters.
Physical Review A, 2015
A one-dimensional quantum oscillator is monitored by taking repeated position measurements. As a first contribution, it is shown that, under a quantum nondemolition measurement scheme applied to a system initially at the ground state: i) the observed sequence of measurements (quantum tracks) corresponding to a single experiment converges to a limit point, and that ii) the limit point is random over the ensemble of the experiments, being distributed as a zero-mean Gaussian random variable with a variance at most equal to the ground state variance. As a second contribution, the richer scenario where the oscillator is coupled with a frozen (i.e., at the ground state) ensemble of independent quantum oscillators. A sharply different behavior emerges: under the same measurement scheme, here we observe that the measurement sequences are essentially divergent. Such a rigorous statistical analysis of the sequential measurement process might be useful for characterizing the main quantities that are currently used for inference, manipulation and monitoring of many quantum systems. Several interesting properties of the quantum tracks evolution, as well as of the associated (quantum) threshold crossing times are discussed, and the dependence upon the main system parameters (e.g., the choice of the measurement sampling time, the degree of interaction with the environment, the measurement device accuracy) are elucidated. At a more fundamental level, it is seen that, as an application of basic Quantum Mechanics principles, a sharp difference exists between the intrinsic randomness unavoidably present in any quantum system, and the extrinsic randomness arising from the environmental coupling, i.e., the randomness induced by an external source of disturbance.
Recovering classical dynamics from coupled quantum systems through continuous measurement
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Equilibration by quantum observation
New Journal of Physics, 2010
We consider an unexplored regime of open quantum systems that relax via coupling to a bath while being monitored by an energy meter. We show that any such system inevitably reaches an equilibrium (quasi-steady) state controllable by the effective rate of monitoring. In the non-Markovian regime, this approach suggests the possible 'freezing' of states, by choosing monitoring rates that set a non-thermal equilibrium state to be the desired one. For measurement rates high enough to cause the quantum Zeno effect, the only steady state is the fully mixed state, due to the breakdown of the rotating wave approximation. Regardless of the monitoring rate, all the quasi-steady states of an observed open quantum system live only as long as the Born approximation holds, namely the bath entropy does not change. Otherwise, both the system and the bath converge to their fully mixed states.