Conditional Hamiltonian and reset operator in the quantum jump approach

Hegerfeldt, Gerhard C.; Sondermann, Dirk G

doi:10.1088/1355-5111/8/1/010

Cited by 54 publications

(41 citation statements)

References 39 publications

(46 reference statements)

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“…The laser field does not appear in the reset state, just as in the case of a single atom [27,30], since its effect during the short time ∆t is negligible. By a simple calculation one checks that Eq.…”

Section: Appendixmentioning

confidence: 99%

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Transition from antibunching to bunching for two dipole-interacting atoms

Beige

Hegerfeldt

1998

Phys. Rev. A

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Section: Appendixmentioning

confidence: 99%

“…For a general N-level system these have been derived in Refs. [27,30]. The derivation of the former is adapted here to a system of two atoms.…”

Section: Appendixmentioning

confidence: 99%

Transition from antibunching to bunching for two dipole-interacting atoms

Beige

Hegerfeldt

1998

Phys. Rev. A

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“…The problem of the effect of repeated * shrabantidhar@gmail.com measurements, made at finite time intervals, on the evolution of a quantum system has been studied in various contexts both theoretically and experimentally [28][29][30][31][32][33]. Because of the probabilistic nature of the quantum detection process, we expect the time of detection to be a stochastic variable.…”

Section: Introductionmentioning

confidence: 99%

Detection of a quantum particle on a lattice under repeated projective measurements

et al. 2015

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We consider a quantum particle, moving on a lattice with a tight-binding Hamiltonian, which is subjected to measurements to detect it's arrival at a particular chosen set of sites. The projective measurements are made at regular time intervals τ , and we consider the evolution of the wave function till the time a detection occurs. We study the probabilities of its first detection at some time and conversely the probability of it not being detected (i.e., surviving) up to that time. We propose a general perturbative approach for understanding the dynamics which maps the evolution operator, consisting of unitary transformations followed by projections, to one described by a nonHermitian Hamiltonian. For some examples, of a particle moving on one and two-dimensional lattices with one or more detection sites, we use this approach to find exact expressions for the survival probability and find excellent agreement with direct numerical results. A mean field model with hopping between all pairs of sites and detection at one site is solved exactly. For the one-and two-dimensional systems, the survival probability is shown to have a power-law decay with time, where the power depends on the initial position of the particle. Finally, we show an interesting and non-trivial connection between the dynamics of the particle in our model and the evolution of a particle under a non-Hermitian Hamiltonian with a large absorbing potential at some sites.

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“…More details as well as applications can be found in Refs. [4,6,9,10,11,12] and in the surveys [13,14].…”

Section: Repeated Gedanken Measurements On a Single System: Jumps Andmentioning

confidence: 99%

“…The general reset state for systems at rest has been determined in Refs. [6,12] and is given in the next section. It may depend on |ψ A (t 1 ) where t 1 is the detection time of the photon.…”

Section: Repeated Gedanken Measurements On a Single System: Jumps Andmentioning

confidence: 99%