The Quantum Jump Approach and Quantum Trajectories

Hegerfeldt, Gerhard C.

doi:10.1007/3-540-44874-8_13

Cited by 11 publications

(3 citation statements)

References 19 publications

(14 reference statements)

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“…An example for such a model would be the detection by means of laser induced fluorescence. In that case, the reset state after the detection of the first fluorescence photon explicitely incorporates a recoil due to the momentum of the emitted photon [25]. It appears reasonable that in the present model no such recoil on the particle occurs: After all, the boson is emitted not by the particle but by the spin lattice.…”

Section: The Continuum Limitmentioning

confidence: 76%

Passage-time distributions from a spin-boson detector model

2007

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The passage-time distribution for a spread-out quantum particle to traverse a specific region is calculated using a detailed quantum model for the detector involved. That model, developed and investigated in earlier works, is based on the detected particle's enhancement of the coupling between a collection of spins (in a metastable state) and their environment. We treat the continuum limit of the model, under the assumption of the Markov property, and calculate the particle state immediately after the first detection. An explicit example with 15 boson modes shows excellent agreement between the discrete model and the continuum limit. Analytical expressions for the passage-time distribution as well as numerical examples are presented. The precision of the measurement scheme is estimated and its optimization discussed. For slow particles, the precision goes like E −3/4 , which improves previous E −1 estimates, obtained with a quantum clock model.

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Section: The Continuum Limitmentioning

confidence: 76%

Passage-time distributions from a spin-boson detector model

2007

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“…[11] Thus, each time step in our simulations corresponds to us conducting a gedanken broadband photon measurement in a window of time δt, over all space and with ideal detectors. [25] It should be noted that the correspondence of jumps to such measurable properties is not the case for all systems, such as the example of two-level relaxation with dephasing given by Mølmer et al [13] Thus, in general one must be wary before prescribing physical meaning to the jumps. Remarkably, modern experimental techniques allow for tight enough monitoring of small open quantum systems so as for the above discussion to be more than just idealised.…”

Section: Measurement Theory and Physical Interpretationmentioning

confidence: 99%

The quantum jump method: photon statistics and macroscopic quantum jumps of two interacting atoms

McDermott¹

2022

Preprint

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We first use the quantum method to replicate the well-known results of a single atom relaxing, whilst demonstrating the intuitive picture it provides for dissipative dynamics. By use of individual "quantum trajectories", the method allows for simulation of systems inaccessible to ensemble treatments. This is shown by replicating resonance fluorescence, allowing us to concurrently demonstrate the method's facilitation of calculating photon statistics by the creation of discrete photon streams.To analyse these, we solidify the theoretical basis for, and implement, a computational method of calculating second-order coherence functions. A process by which to model interacting two-atom systems to allow for computation with the quantum jump method is then developed. Using this, we demonstrate cooperative effects leading to greatly modified emission spectra, before investigating the decoupling of states from dissipative and coherent interactions. Here, we find the novel insight provided by the quantum jump method both births and provides the tools with which to begin an investigation into the occurrence of macroscopic jumps and the formation of macroscopic dark periods in a system of two two-level dipole-dipole coupled atoms.

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“…describing the time evolution until the emission of the first photon in the framework of the quantum jump approach [80]. Here, γ is the decay rate of the excited level and ∆ is the detuning of the laser.…”

Section: The Dipole Forcementioning

confidence: 99%

Effects of Atom-Laser Interaction on Ultra-Cold Atoms

Martin¹

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In the first part of this work cooperative effects in the fluorescence of dipole-dipole interacting atoms in a trap are studied. When illuminated by lasers, single trapped atoms which possess a metastable state in their effective level scheme, may, under certain conditions, exhibit macroscopic dark periods in their fluorescence signal. The spontaneous emission abruptly ceases for a certain period of time. In a simplified picture, this can be explained as a shelving of the electron in the metastable state. If

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The Quantum Jump Approach and Quantum Trajectories

Cited by 11 publications

References 19 publications

Passage-time distributions from a spin-boson detector model

Passage-time distributions from a spin-boson detector model

The quantum jump method: photon statistics and macroscopic quantum jumps of two interacting atoms

Effects of Atom-Laser Interaction on Ultra-Cold Atoms

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