Spontaneous emission from an extended wavepacket

Rza̧żewski, Kazimierz; Żakowicz, W.

doi:10.1088/0953-4075/25/13/001

Cited by 37 publications

(31 citation statements)

References 8 publications

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“…In this case the degrees-offreedom of the electromagnetic field play the role of a reservoir to which the atoms are coupled. Since it is known that usually the center-of-mass motion of the atoms has only a small influence on the spontaneous emission rate [6,7] we neglect it alltogether and use the atomic Hamiltonian…”

Section: Decoherence Of the Atomic Field Operatormentioning

confidence: 99%

Decoherence of atomic gases in largely detuned laser fields

Marzlin

2001

Phys. Rev. A

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We study theoretically the decoherence of a gas of bosonic atoms induced by the interaction with a largely detuned laser beam. It is shown that for a standing laser beam decoherence coincides with the single-particle result. For a running laser beam many-particle effects lead to significant modifications. 03.65.Yz, 03.75.Fi In experiments with atomic Bose-Einstein condensates [1,2] the trap which is used to isolate the atoms from the environment plays an important role for the physical behaviour of the system. In a magnetic trap usually only atoms with a specific magnetic hyperfine quantum number are stored. An optical trap [3] can be used to confine atoms in all Zeeman sublevels. However, in order to preserve the atomic coherence spontaneous emission of photons must be avoided. A large detuning ∆ of the laser beams providing the trap field reduces the excitation probability for atoms and thus reduces the number of spontaneously emitted photons. At the same time, a relatively strong intensity of the laser beams, and correspondingly a large Rabi frequency Ω(x), ensures that the laser beams' effect is still large enough to produce a strong potential for the atoms.The aim of this paper is to examine light-induced decoherence of a gas of ultracold atoms in an optical trap and to deduce the influence of atomic many-particle properties on this decoherence. To do so we study solutions to a master equation for reduced Heisenberg operators describing a quantum field of bosonic two-level atoms interacting with a detuned laser beam and the vacuum fluctuations of the electromagnetic field. The technique of reduced Heisenberg operators has previously been employed by Nemoto and Shibata [4] and allows an elegant description of decoherence in a many-particle context. After the derivation of the master equation we will adiabatically eliminate the excited state to get an effective master equation for the atomic internal ground state. The main result of the paper is that many-particle effects lead to a nonlocal modification of light-induced decoherence that vanishes for laser fields with spatially homogeneous phase (e.g., a standing laser wave) but makes substantial contributions for a running laser wave. Derivation of the master equation:We consider a general system that is described by the direct product of two Hilbert spaces H S and H R , where H S describes the open system that we are interested in, and H R describes the reservoir to which the system is coupled. It is our aim to find a master equation describing the evolution of reduced Heisenberg operators for the system only. We define a reduced Heisenberg operatorR S by the relationRwhereR(t) is the original Heisenberg operator which acts on H S ⊗ H R andρ R is the density matrix describing the state of the reservoir. It is thereby assumed that the (time-independent) density matrix can be written in the formρ =ρ S ⊗ρ R so that there are initially no correlations between the system and the reservoir. The physical significance of the reduced Heisenberg operator is that i...

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Section: Decoherence Of the Atomic Field Operatormentioning

confidence: 99%

Decoherence of atomic gases in largely detuned laser fields

Marzlin

2001

Phys. Rev. A

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“…Different types of modifications are caused by the motion of atoms as a whole by means of the coupling between internal radiative transitions and the center-of-mass motion through the recoil [3]. In a recent paper [4] we found a significant modification of the spontaneous emission line shape due to the shape of the freely moving atomic wave packet. The structure found is a direct signature of the shape of the atomic wave packet in the momentum space.…”

Section: Introductionmentioning

confidence: 77%

“…A simple exercise shows that the total intensity of light emitted in a given direction again [4] practically does not differ from the standard dipole pattern hidden in the angular dependence of the coupling constant A. . .…”

Section: 17)mentioning

confidence: 94%

Spontaneous emission from a trapped atom

Stoop

Rza̧żewski

1995

Phys. Rev. A

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“…The appropriate photon-atom amplitude in this case was derived by Rza¸_ z zewski and _ Z Zakowicz [2] in 1992 to examine spontaneous emission lineshapes of moving atoms and extended by Rza¸_ z zewski and Stoop [3]. The joint amplitude is not factorable; that is, it entangles the photon with the emitting atom.…”

Section: Photon-atom Entanglementmentioning

confidence: 99%

“…The Rza¸_ z zewski-_ Z Zakowicz [2] amplitude under discussion is easily written as a function of emitted photon wave vector k and recoiling atom wave vector q in the long-time limit of the Weisskopf-Wigner essential states approximation in the form Cðk; qÞ ¼ gðkÞ exp Àðq þ kÞ 2 = 2 0 Â Ã…”

Section: Photon-atom Entanglementmentioning

confidence: 99%

Einstein localization in entangled light scattering

Chan

Law

Федоров

et al. 2004

Journal of Modern Optics

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We discuss Einstein-Podolsky-Rosen (EPR)-type entanglement in two-particle break-up, using Raman scattering with atom recoil as an example. The Schmidt number K is used as a measure of entanglement and the conditions to acquire high entanglement are obtained. We also illustrate the EPR conditional uncertainty in a situation where Dx Dp reaches a value much smaller than the Heisenberg limit. Photon-atom entanglementIn the famous Einstein-Podolsky-Rosen (EPR) [1] paper of 1935 a physical system undergoes fission, and breaks up into two daughter particles flying from each other into remote locations, connected only by energy and momentum conservation. Here we report calculations for an EPR analogue in which observation of Einstein-type localization with high entanglement may be possible.The process of spontaneous emission of a photon by an atom is one obvious analogue of the EPR scenario if atomic recoil is included. The appropriate photon-atom amplitude in this case was derived by Rza¸_ z zewski and _ Z Zakowicz [2] in 1992 to examine spontaneous emission lineshapes of moving atoms and extended by Rza¸_ z zewski and Stoop [3]. The joint amplitude is not factorable; that is, it entangles the photon with the emitting atom. We have made use of this amplitude in our recent investigations of photon wave functions and photon-atom entanglement [4,5] and analogues have been noted in other contexts [6,7].The Rza¸_ z zewski-_ Z Zakowicz [2] amplitude under discussion is easily written as a function of emitted photon wave vector k and recoiling atom wave vector q in the long-time limit of the Weisskopf-Wigner essential states approximation in the formwhere g is a slowly varying function of photon momentum, is the atomic radiative half-linewidth, and the Gaussian function is the initial probability Journal of Modern Optics

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Spontaneous emission from an extended wavepacket

Cited by 37 publications

References 8 publications

Decoherence of atomic gases in largely detuned laser fields

Decoherence of atomic gases in largely detuned laser fields

Spontaneous emission from a trapped atom

Einstein localization in entangled light scattering

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