Stochastic initiation of superradiance in a cavity: An approximation scheme within quantum trajectory theory

Clemens, James; Carmichael, H. J.

doi:10.1103/physreva.65.023815

Cited by 23 publications

(34 citation statements)

References 31 publications

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“…From |J = 0, M = 0 the atoms can only be pumped to |J = 1, M = 1 from which they relax to |J = 1, M = −1 by rapidly emitting a pair of photons in a cascade within a time of order Γ −1 c . In the superradiant regime for intermediate pumping g (2) (0) is reduced to a value about half way between 1 and 2. It reaches a minimum at the superradiant emission maximum, w = N Γ c /2.…”

Section: Resultsmentioning

confidence: 99%

“…This histogram is closely related to the conditional probability P (t + j∆t|t) to find a second photon at time t + j∆t provided that a first photon has been detected at time t, i.e.n j (∆t) = ∆tP (t + j∆t|t). Using the relation between that conditional probability and the joint probability, P 2 (t, t + j∆t) = P (t + j∆t|t)P 1 (t), we can then find g (2) (j∆t) on a grid with spacing ∆t according to…”

Section: Hanbury-brown-twiss Signalmentioning

confidence: 99%

“…(10) we have also made use of the result from the inputoutput theory for cavities that normally ordered correlation functions outside of a cavity are equal to the normally ordered correlation functions of the intra-cavity field, provided that the input ports of the cavity are in vacuum states [21,22]. The second order correlation function at zero time delay, g (2) (0), is related to the fluctuations ∆I 2 = Î 2 − Î 2 of the out-coupled photon fluxÎ. These fluctuations ∆I 2 can be used to characterize the instability of the intensity of the out-coupled beam becauseÎ is proportional to the beam intensity.…”

Section: Hanbury-brown-twiss Signalmentioning

confidence: 99%

“…The noise properties of the light emitted in superradiance have been of particular interest. This is because the early stages of superradiance are often initiated by quantum fluctuations which are subsequently amplified by the collective emission process [1,2]. Superradiance can thus serve as a physical phenomenon that allows us to study the microscopic quantum fluctuations through their macroscopic consequences.…”

Section: Introductionmentioning

confidence: 99%

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Intensity fluctuations in steady-state superradiance

2010

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Alkaline-earth like atoms with ultra-narrow optical transitions enable superradiance in steady state. The emitted light promises to have an unprecedented stability with a linewidth as narrow as a few millihertz. In order to evaluate the potential usefulness of this light source as an ultrastable oscillator in clock and precision metrology applications it is crucial to understand the noise properties of this device. In this paper we present a detailed analysis of the intensity fluctuations by means of Monte-Carlo simulations and semi-classical approximations. We find that the light exhibits bunching below threshold, is to a good approximation coherent in the superradiant regime, and is chaotic above the second threshold.

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Section: Resultsmentioning

confidence: 99%

Section: Hanbury-brown-twiss Signalmentioning

confidence: 99%

Section: Hanbury-brown-twiss Signalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Intensity fluctuations in steady-state superradiance

2010

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“…To explore these collective effects, many new ideas, such as the quantum jump approach, were developed to treat superradiance [16,17,18]. Recently, we successfully incorporated cooperative effects into a novel formalism for optically dense media.…”

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confidence: 99%

Superradiance in ultracold Rydberg gases

et al. 2007

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Experiments in dense, ultracold gases of rubidium Rydberg atoms show a considerable decrease of the radiative excited state lifetimes compared to dilute gases. This accelerated decay is explained by collective and cooperative effects, leading to superradiance. A novel formalism to calculate effective decay times in a dense Rydberg gas shows that for these atoms the decay into nearby levels increases by up to three orders of magnitude. Excellent agreement between theory and experiment follows from this treatment of Rydberg decay behavior.In recent years, ultracold atomic gases have been used to probe a variety of many-body phenomena such as Bose-Einstein condensation [1,2] and degenerate Fermi gases [3]. In addition to collective effects due to particle statistics, other manifestations of many-body physics have been explored, such as in slow-light experiments [4] and in ultracold Rydberg gases (e.g. the diffusion of excitations through resonant collisions [5] and the blockade mechanism [6]). Another important fundamental collective effect is superradiance, in which photon exchange between atoms modifies the behavior of the sample. In particular, cooperative effects due to virtual photon exchange can lead to the formation of so called Dicke states [7]. These states are the symmetric superposition of all states with the same total excitation level for constant atom number N . Interest in Dicke states has grown recently because of their potential advantages in quantum information processing [8] and their importance in the behavior of Bose-Einstein condensates [9].In this Letter, we are interested in many-body physics involving photon exchange in an ultracold gas of Rydberg atoms. Because superradiance depends on the atomic density per cubic wavelength, and because radiative decay of Rydberg atoms takes place predominantly between the closely spaced upper levels, ultracold Rydberg gases are ideal systems to study superradiance. In fact, Rydberg atoms have many interesting properties: their size can become comparable to the atomic separation, and they have huge dipole moments ℘ ∼ n 2 , where n is the principal quantum number of the Rydberg state. In addition, for long-wavelength transitions between neighboring states of high n the "cooperative parameter" C = N λ 3 /4π 2 (where N is the density of atoms, λ is the transition wavelength), is large for Rydberg atoms, which means collective effects are much easier to obtain than for ground-state atoms [10]. This was confirmed in earlier experiments for Rydberg atoms at high [11,12] and low temperatures [13]. Note that these many-body effects may pose a limit on the measurement of lifetimes of Rydberg atoms [14] and may cause undesirable frequency shifts, for example in atomic clocks [15].The source responsible for both virtual and real photon exchange is the dipole-dipole interaction. It governs the build-up as well as the decay of coherence in a dense radiating sample. On the one hand, the virtual exchange of photons is responsible for the so-called exchange interaction. ...

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Superradiance: An Integrated Approach to Cooperative Effects in Various Systems

Lin

Yelin

2012

Advances in Atomic, Molecular, and Optical Physics

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Stochastic initiation of superradiance in a cavity: An approximation scheme within quantum trajectory theory

Cited by 23 publications

References 31 publications

Intensity fluctuations in steady-state superradiance

Intensity fluctuations in steady-state superradiance

Superradiance in ultracold Rydberg gases

Superradiance: An Integrated Approach to Cooperative Effects in Various Systems

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