Monitoring the wave function by time continuous position measurement

Abstract

We consider a single copy of a quantum particle moving in a potential and show that it is possible to monitor its complete wave function by only continuously measuring its position. While we assume that the potential is known, no information is available about its state initially. In order to monitor the wave function, an estimate of the wave function is propagated due to the influence of the potential and continuously updated according to the results of the position measurement.We demonstrate by numerical simulations that the estimation reaches arbitrary values of accuracy below 100% within a finite time period for the potentials we study. In this way our method grants, a certain time after the beginning of the measurement, an accurate real-time record of the state evolution including the influence of the continuous measurement. Moreover, it is robust against sudden perturbations of the system as for example random momentum kicks from environmental particles, provided they occur not too frequently.

Quantum signatures in the quantum Carnot cycle

“…relax to a diagonal state in the energy representation and coherence vanishes. The back action of the weak measurement is therefore equivalent to pure dephasing [60,61], described by the master equation:…”

“…Pure dephasing is introduced during the adiabats of the Endo-global cycle to evaluate the importance of coherence in the engine operation. Such dephasing can be caused by noise in the driving field and weak measurement [61,[73][74][75]. A Lindbladian describing dephasing is added to the free dynamics.…”

Maintaining quantum coherence in the presence of noise through state monitoring

“…In that scheme, the evolving state of the system, as well as an estimate of that state, and the measurement readout are described by three coupled stochastic differential equations, which indicate that the state estimate converges to the real state for a broad class of systems; cf. [9]. Continuous measurements have also been shown to drive statistical mixtures of spatial wave packets into pure states, which can be entirely determined by the measurement record alone [10].…”

Equation of motion for estimation fidelity of monitored oscillating qubits

“…[2], in the case where the Hamiltonian is precisely known (δ = 0) the above update follows the spirit of the classical Bayesian update and we expect intuitively that the measured actual |ψ and the updated estimate |ψ e come "closer" to each other. The method performs suitably well in various quantum estimation situations [4,11,14,19]. In what follows, we will use Eq.…”

“…The state estimate * konradt@ukzn.ac.za † hermann.uys@gmail.com is sequentially updated based on the outcome of each measurement on the actual quantum state with the same propagator as the system. Numerical simulations have demonstrated the convergence of the state estimate when all parameters in the Hamiltonian are precisely known [4,14] and even for the case of process tomography, treating the Hamiltonian parameters as state variables of a hybrid system [15][16][17].…”