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Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)

Collision of an atom with a colored vacuum: the vacuum-induced Kapitza-Dirac effect

Young-Tak Chough, Jung Bog Kim, Kyungwon An

Published Jan 20, 2003• 0 citations
Publisher

Abstract

We address a somewhat naive but intriguing question of momentum transfer between a matter particle and a standing-wave mode of electromagnetic radiation. A beam of two-state atoms prepared in the upper-state enters at a slightly tilted angle from the normal direction to the axis of a single mode cavity. A similar setup with a relatively short atom-field interaction time was considered by the MIT group in their microlaser experiment, where the microlaser output was measured as a function of the atom-cavity detuning, revealing two-peak gain spectra. In our present consideration, however, the atom-cavity interaction time is appropriately set that by the time an atom leaves the interaction region, it has undergone a Rabi flip. The cavity is slightly detuned from the atomic resonance frequency that each radiation quantum released from the Rabi flip of the atoms is expected to be launched into only one of the two possible directions in which the resonance condition is met by the Doppler shift due to the transverse velocity component of the atom.

DOI
10.1109/cleopr.1999.811590

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Annual Meeting Optical Society of America•Jan 1, 1991•0 citations
We address a somewhat naive but intriguing question of momentum transfer between a matter particle and a standing-wave mode of electromagnetic radiation. A beam of two-state atoms prepared in the upper-state enters at a slightly tilted angle from the normal direction to the axis of a single mode cavity. A similar setup with a relatively short atom-field interaction time was considered by the MIT group in their microlaser experiment, where the microlaser output was measured as a function of the atom-cavity detuning, revealing two-peak gain spectra. In our present consideration, however, the atom-cavity interaction time is appropriately set that by the time an atom leaves the interaction region, it has undergone a Rabi flip. The cavity is slightly detuned from the atomic resonance frequency that each radiation quantum released from the Rabi flip of the atoms is expected to be launched into only one of the two possible directions in which the resonance condition is met by the Doppler shift due to the transverse velocity component of the atom.
Deflection of an inverted two-state atom by a standing-wave cavity vacuum is analyzed. It is shown that clean vacuum Rabi oscillations occur at a frequency of g0/2{g}_{0}/2g0​/2 between the initial atom-field state and the state with the atomic transverse momentum displaced by $\ensuremath{\Elzxh}k$ if the cavity is tuned to the Doppler shift associated with the atomic motion along the cavity axis, given that the shift is much larger than the optimum atom-cavity coupling constant g0.{g}_{0}.g0​. Consequently, the atom can be deflected by the cavity, the direction of which is precisely controlled by the atom-cavity detuning.
We use a basis of Bloch wave functions to solve the problem of spontaneous emission from an atom inside a standing-wave cavity. In this way we incorporate the effects of the atom’s quantized center-mass-motion in the periodic light-force potential of the one-quantum dressed states during the spontaneous emission process. We calculate emission spectra and the momentum distribution of the atom. Under strong-coupling conditions, “vacuum” Rabi spectra become asymmetric, with an increased relative weight given to the red side of the spectrum because of the transfer of energy to the center-of-mass motion of the atom. Because of the nonperturbative interaction between the atom and the cavity mode, many momentum quanta are transferred to the atom from the cavity mirrors during the irreversible emission of just one photon. Thus, the atom is diffracted by its own radiation reaction field. We analyze these effects using the Bloch-state basis. Use of the secular approximation provides a simple rate equation description of transitions from the Bloch states excited in the initial state to the atom-cavity ground state. We compare this approach with other ways of doing the calculations and discuss the accuracy of the secular approximation. We consider the extension of these calculations to treat the effects of photon statistics on the momentum distribution of atoms traversing a standing-wave cavity.
We study the amplification of a resonant standing-wave light field due to the interaction with a beam of monovelocity two-level atoms moving in the Raman-Nath regime and in the Bragg regime. The atomic density is low so that, at most, one atom is inside the cavity at a time. This system is very similar to the well-known micromaser but it is operating in the optical region of the field frequencies. Therefore, the situation corresponds to a microlaser. Unlike the micromaser system, the momentum transfer between the atoms and photons in the microlaser essentially effects the center-of-mass motion of the atoms and the evolution of the field.
We discuss two possible processes that may lead to unidirectional momentum transfer to atoms from a near-resonant standing-wave light field. The first is Bragg scattering of the matter waves from the tilted light grating—this process leaves the atoms unexcited. The second is a multiphoton (Doppleron) process in which the atom, by sequential absorption/emission of photons from/into the two traveling-wave components of the standing wave (which appear at different frequencies owingto the motion of the atom in the field), can complete the energy resonance condition for excitation to its excited state. Detailed consideration of the inteferring process of spontaneous emission and experimental factors such as the interplay among interaction length, angular collimation of the standing wave, and transit-time frequency broadening of the light frequency show that the two processes are both potentially observable but under considerably different experimental conditions.
An exact solution for the problem of two two-level atoms interacting with a single-mode detuned quantized radiation field is presented. On resonance, an asymptotic result is derived for large coherent initial fields. It is shown that when the atoms are initially prepared in one of the semiclassical eigenstates, the atom-plus-field wavefunction remains almost factored into an atomic and a field part throughout the interaction. Under certain conditions, the atomic part evolves into a unique pure state at half-revival time. The effects of the cavity detuning on the dynamics of the atomic level occupation probabilities and emission spectra are studied. It is found, for non-symmetrical excitation, that far off-resonance the field acts like a virtual level by means of which the energy is transferred between the atoms. Due to non-zero detuning, nine-peaked spectra are observed and are given a clear explanation from the dressed-state viewpoint. It is established that in the case of symmetrical excitation, the intensity of the emission spectrum is two times larger than that in the case of non-symmetrical excitation.
The boundary conditions imposed on the vacuum field by the superconfocal cavity (SCC) create a region of space, the active volume, at the cavity center in which the spectral structure of the vacuum field is perturbed. These perturbations transform the normally white spectrum of the free-space vacuum field into a colored vacuum whose spectrum is a comb of peaks coincident with the cavity resonance frequencies. Operating as designed, atoms resonant with the cavity and in the active region will experience a vacuum field mode density 1.5 times that in free-space. Perturbations in the vacuum field mode density of this magnitude and operative over so large an active volume (1.4 × 107µm3) have not, to our knowledge, been previously achieved in an open optical cavity. We expect to observe a plethora of new and novel phenomena associated with laser–atom interactions in the presence of a colored vacuum. The first experiment will focus on the dynamic suppression of spontaneous emission1 which predicts a dramatic narrowing of the central Mollow peak as the Rabi frequency becomes larger than the FWHM of the SCC-induced peaks in the vacuum field mode density.