Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Quantum theory of a micromaser operating on the atomic scattering from a resonant standing wave

Farhan Saif, Fam Le Kien, Muhammad Suhail Zubairy

Published Sep 18, 2001• 13 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.64.043812

Related papers

Influence of Atomic Motion on a Microlaser in an Optical Standing-Wave Cavity

Jingtao Zhang, Feng Xun-Li, Zhang Wen-Qi +1 more

We study the microlaser in an optical standing-wave cavity injected with two-level atoms. The results have shown the obvious influence of atomic centre-of-mass motion on the microlaser, such as the photon distribution, the linewidth and the frequency shift. It was found that when the momentum of atoms is comparable to that of photons, the influence of atomic motion is dominated and the number of photons in the microlaser can be greatly enhanced, owing to part of the atomic kinetic energy being transferred to the resonator. This work provides a comparison of the related studies on the atomic motion under special assumptions.

Chinese Physics Letters•Apr 18, 2002•4 citations

Microlaser: a fundamental quantum generator of light

Kyungwon An, Ramachandra Rao Dasari, Michael S. Feld

We have achieved the first realization of a single atom microlaser, a laser oscillator with only one atom in an optical resonator. In the experiment a beam of two-level barium atoms traverses an ultrahigh Q single-mode cavity. The atoms are inverted by a (pi) -pulse field before they enter the cavity. Laser oscillation ((lambda) equals 791 nm) has been observed, with the mean number of atoms inside the mode <N> as small as 0.1, resulting in the mean number of photons in the mode <N> or 0.14. To understand the results quantitatively we used a fully-quantized one-atom microlaser theory adapted from its counterpart micromaser theory. The present theory was found to be in good agreement with the data for small <N> and <n>. Discrepancy between experiment and theory was observed for <n> very much greater than 1 and <N> approximately equal to 1. This discrepancy may be explained by the standing-wave nature of the cavity mode, in combination with the saturation effect occurring at large cavity photon number, as well as by the breakdown of single-atom interaction assumption in the theory for <N> greater than or equal to 1.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 6, 1996•2 citations

Coherent scattering of an atom in the field of a standing wave under conditions of initial quantum correlation of subsystems

Andrew I. Trubilko

Coherent scattering of a two-level atom in the field of a quantized standing wave of a micromaser is considered under conditions of initial quantum correlation between the atom and the field. Such a correlation can be produced by a broadband parametric source. The interaction leading to scattering of the atom from the nonuniform field occurs in the dispersion limit or in the wing of the absorption line of the atom. Apart from the quantized field, the atom simultaneously interacts with two classical counterpropagating waves with different frequencies, which are acting in the plane perpendicular to the atom’s propagation velocity and to the wavevector of the standing wave. Joint action of the quantized field and two classical waves induces effective two-photon and Raman resonance interaction on the working transition. The effective Hamiltonian of the interaction is derived using the unitary transformation method developed for a moving atom. A strong effect is detected, which makes it possible to distinguish the correlated initial state of the atom and the field in the scattering of atom from the state of independent systems. For all three waves, scattering is not observed when systems with quantum correlation are prepared using a high-intensity parametric source. Conversely, when the atom interacts only with the nonuniform field of the standing wave, scattering is not observed in the case of the initial factorized state.

Journal of Experimental and Theoretical Physics•Oct 1, 2016•6 citations

Raman-Nath and Bragg scattering in atomic deflection

Ewan M. Wright, Scott Alan Glasgow, Pierre Meystre

The deflection of a stream of two-level atoms by a standing-wave light field has recently been studied extensively both experimentally and theoretically due to potential use in constructing an atomic inter ferometer with the De Broglie wavelength as its resolution limit.1 Recent experiments have shown the existence of at least two scattering regimes, namely, the Raman-Nath regime2 in which multiple atom ic beams can arise and the Bragg regime3 in which only two coherent beams participate.

•May 21, 1990•0 citations

Atomic beam deflection in a quantum field

Pierre Meystre, E. Schumacher, Stig Stenholm +1 more

We investigate to which extent the quantum nature of light modifies laser-induced atomic beam deflection in a plane standing wave. Our model considers a single two-level atom interacting with a single quantized standing wave mode of the electromagnetic field. We neglect spontaneous emission into other field modes, an approximation valid for short enough times. We find that there is an essential qualitative difference between the cases of a coherent field and a thermal field. For a coherent field, the atomic momentum distribution after interaction has two symmetric peaks on the wings and resembles the semiclassical result of Arimondo et al. [Phys. Rev. A 24, 898 (1981)]. For a thermal field, this distribution has its maximum at p = 0. It is characterized by a constant contribution at p = 0, some sharp interference features, and near-Gaussian wings. The only feature common to both cases is that in the Raman-Nath regime of scattering, the range on transverse momenta grows linearly with time at a rate proportional to 〈 n 〉 , where 〈 n 〉 is the mean number of photons in the field.

Annual Meeting Optical Society of America•Jan 1, 1989•3 citations

Deflection of Resonant Multilevel Particles in a Standing Wave Light Field

�. Lindberg

We study the deflection of an atomic system with a resonant multilevel energy structure in classical and quantized wave light fields. We obtain that the shape of the momentum distribution is very sensitive to the energy level structure, whereas its moments are not. Comparison with a two-level case is made. PACS: 32.80, 33.80, 42.50 During the last two decades a remarkable development in mechanically manipulating atomary particles with resonant laser light has taken place (for a review, see for example [1, 2] and references therein). In addition to trapping and cooling of particles, the deflection of particles by a laser beam offers interesting possibilities, for example, to construct atomic interferometers or beam splitters [2-4]. This problem has been studied extensively both theoretically [2, 5, 8] and experimentally [9-12]. The fact that the momentum distribution caused by the scattering is connected to the quantum statistical properties of the scattered light has been known for some time [13]. Recently, one has also realized that the quantum statistics of the light causing the scattering can be important [14]. At low photon numbers, for example, the initial field state strongly influences the resulting momentum distribution. A related effect is that a standing wave and two counterpropagating traveling plane waves of equal emplitudes cause a different diffraction pattern when fields are treated quantum mechanically [15]. Most previous work on the deflection of particles by light fields used two-level atoms. In this paper we study how resonant multilevel systems scatter when they traverse a plane wave. In practical applications, molecules or highly excited atoms have similar energy structures as the models we use in this work. In most cases, we assume that the Raman-Nath regime is valid, i.e., the kinetic energy of the particle can be neglected. However, the field coupling is assumed to be sufficiently strong to make multiple scattering events possible. Our results show that the final momentum distribution of a multi-level system can strongly deviate from that of a two-level atom. It is of interest that the momentum distributions for resonant ladder systems are in general superpositions of few or several distributions similar to that of a two-level system. We also study the expectation values related to the momentum distribution and show that the spread in momentum is remarkably independent of the system considered. The absorption and reabsorption of photons during the scattering process causes the photon distribution to be smoothed out, and for long times a steady state is reached. The cases we studied did not show a creation of sub-Poissonian light. Our model and assumptions are described and discussed in Sect. 1. Some of the general properties of the momentum distribution are discussed in Sect. 2. In Sect. 3 we derive the generating function of the moments of momentum change in Raman-Nath regime. The main part of the paper is contained in Sects. 4 and 5, in which the momentum distribution itself is discussed for several model systems. In Sect. 4 a semiclassical field is assumed and in Sect. 5 a quantum field is used. The effects of the scattering on the field photon statistics are studied in Sect. 6. The final discussion of the results is given in Sect. 7.

•Jan 1, 2004•0 citations
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 study the microlaser in an optical standing-wave cavity injected with two-level atoms. The results have shown the obvious influence of atomic centre-of-mass motion on the microlaser, such as the photon distribution, the linewidth and the frequency shift. It was found that when the momentum of atoms is comparable to that of photons, the influence of atomic motion is dominated and the number of photons in the microlaser can be greatly enhanced, owing to part of the atomic kinetic energy being transferred to the resonator. This work provides a comparison of the related studies on the atomic motion under special assumptions.
We have achieved the first realization of a single atom microlaser, a laser oscillator with only one atom in an optical resonator. In the experiment a beam of two-level barium atoms traverses an ultrahigh Q single-mode cavity. The atoms are inverted by a (pi) -pulse field before they enter the cavity. Laser oscillation ((lambda) equals 791 nm) has been observed, with the mean number of atoms inside the mode <N> as small as 0.1, resulting in the mean number of photons in the mode <N> or 0.14. To understand the results quantitatively we used a fully-quantized one-atom microlaser theory adapted from its counterpart micromaser theory. The present theory was found to be in good agreement with the data for small <N> and <n>. Discrepancy between experiment and theory was observed for <n> very much greater than 1 and <N> approximately equal to 1. This discrepancy may be explained by the standing-wave nature of the cavity mode, in combination with the saturation effect occurring at large cavity photon number, as well as by the breakdown of single-atom interaction assumption in the theory for <N> greater than or equal to 1.
Coherent scattering of a two-level atom in the field of a quantized standing wave of a micromaser is considered under conditions of initial quantum correlation between the atom and the field. Such a correlation can be produced by a broadband parametric source. The interaction leading to scattering of the atom from the nonuniform field occurs in the dispersion limit or in the wing of the absorption line of the atom. Apart from the quantized field, the atom simultaneously interacts with two classical counterpropagating waves with different frequencies, which are acting in the plane perpendicular to the atom’s propagation velocity and to the wavevector of the standing wave. Joint action of the quantized field and two classical waves induces effective two-photon and Raman resonance interaction on the working transition. The effective Hamiltonian of the interaction is derived using the unitary transformation method developed for a moving atom. A strong effect is detected, which makes it possible to distinguish the correlated initial state of the atom and the field in the scattering of atom from the state of independent systems. For all three waves, scattering is not observed when systems with quantum correlation are prepared using a high-intensity parametric source. Conversely, when the atom interacts only with the nonuniform field of the standing wave, scattering is not observed in the case of the initial factorized state.
We investigate to which extent the quantum nature of light modifies laser-induced atomic beam deflection in a plane standing wave. Our model considers a single two-level atom interacting with a single quantized standing wave mode of the electromagnetic field. We neglect spontaneous emission into other field modes, an approximation valid for short enough times. We find that there is an essential qualitative difference between the cases of a coherent field and a thermal field. For a coherent field, the atomic momentum distribution after interaction has two symmetric peaks on the wings and resembles the semiclassical result of Arimondo et al. [Phys. Rev. A 24, 898 (1981)]. For a thermal field, this distribution has its maximum at p = 0. It is characterized by a constant contribution at p = 0, some sharp interference features, and near-Gaussian wings. The only feature common to both cases is that in the Raman-Nath regime of scattering, the range on transverse momenta grows linearly with time at a rate proportional to 〈 n 〉 , where 〈 n 〉 is the mean number of photons in the field.
We study the deflection of an atomic system with a resonant multilevel energy structure in classical and quantized wave light fields. We obtain that the shape of the momentum distribution is very sensitive to the energy level structure, whereas its moments are not. Comparison with a two-level case is made. PACS: 32.80, 33.80, 42.50 During the last two decades a remarkable development in mechanically manipulating atomary particles with resonant laser light has taken place (for a review, see for example [1, 2] and references therein). In addition to trapping and cooling of particles, the deflection of particles by a laser beam offers interesting possibilities, for example, to construct atomic interferometers or beam splitters [2-4]. This problem has been studied extensively both theoretically [2, 5, 8] and experimentally [9-12]. The fact that the momentum distribution caused by the scattering is connected to the quantum statistical properties of the scattered light has been known for some time [13]. Recently, one has also realized that the quantum statistics of the light causing the scattering can be important [14]. At low photon numbers, for example, the initial field state strongly influences the resulting momentum distribution. A related effect is that a standing wave and two counterpropagating traveling plane waves of equal emplitudes cause a different diffraction pattern when fields are treated quantum mechanically [15]. Most previous work on the deflection of particles by light fields used two-level atoms. In this paper we study how resonant multilevel systems scatter when they traverse a plane wave. In practical applications, molecules or highly excited atoms have similar energy structures as the models we use in this work. In most cases, we assume that the Raman-Nath regime is valid, i.e., the kinetic energy of the particle can be neglected. However, the field coupling is assumed to be sufficiently strong to make multiple scattering events possible. Our results show that the final momentum distribution of a multi-level system can strongly deviate from that of a two-level atom. It is of interest that the momentum distributions for resonant ladder systems are in general superpositions of few or several distributions similar to that of a two-level system. We also study the expectation values related to the momentum distribution and show that the spread in momentum is remarkably independent of the system considered. The absorption and reabsorption of photons during the scattering process causes the photon distribution to be smoothed out, and for long times a steady state is reached. The cases we studied did not show a creation of sub-Poissonian light. Our model and assumptions are described and discussed in Sect. 1. Some of the general properties of the momentum distribution are discussed in Sect. 2. In Sect. 3 we derive the generating function of the moments of momentum change in Raman-Nath regime. The main part of the paper is contained in Sects. 4 and 5, in which the momentum distribution itself is discussed for several model systems. In Sect. 4 a semiclassical field is assumed and in Sect. 5 a quantum field is used. The effects of the scattering on the field photon statistics are studied in Sect. 6. The final discussion of the results is given in Sect. 7.