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

Deflection of atoms by a resonant standing electromagnetic wave

R. J. Cook, Anthony F. Bernhardt

Published Dec 1, 1978• 135 citations
Publisher

Abstract

Deflection of an atom due to momentum transfer from a strong resonant standing electromagnetic wave is investigated theoretically in the limit of short atom-field interaction time. The translational and internal motions of the atom are treated quantum mechanically, while the field is treated classically. It is shown that momentum transfer from a standing wave to an atom proceeds at the induced or Rabi rate, rather than the spontaneous rate characteristic of radiation pressure. In a typical case, atomic deflections of order 1\ifmmode^\circ\else\textdegree\fi{} are achieved with ${10}^{6}$ W/${\mathrm{cm}}^{2}$ field intensity in a time less than the natural lifetime of the excited atom.

DOI
10.1103/physreva.18.2533

Related papers

Theory of resonance-radiation pressure

Richard J. Cook

A general theory of the motion of a two-level atom in a resonant or near-resonant electromagnetic wave of arbitrary amplitude and phase, including effects of radiative relaxation due to interaction with the quantized vacuum field, is developed from first principles. Particular emphasis is placed on the effects of quantum-mechanical fluctuations of the radiation force and on the associated diffusion of atomic momentum due to spontaneous and induced absorption and emission processes. Analytic results and numerical examples are presented for (1) the lower bound on the temperature achievable by radiation cooling in a standing wave tuned below resonance, (2) the heating rate in a strong resonant standing wave, (3) the maximum confinement time for an atom in a Gaussian radiation trap, (4) the deflection and spreading of an atomic beam transversely illuminated by a strong resonant running wave, and (5) the transverse cooling of an atomic beam by a strong running wave tuned below resonance.

Physical Review A•Sep 1, 1980•131 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 atoms by standing-wave radiation

Philip E. Moskowitz, P. L. Gould, David E. Pritchard

We have observed momentum transfer from a standing-wave light field to an atomic beam. The atomic beam is split symmetrically into two peaks whose separation increases with field strength. The short interaction time ensures that this deflection is due to induced forces; these are described using a semiclassical dressed-atom treatment, which gives good agreement with the data. In addition to the splitting, we have observed diffraction of the atomic beam due to the exchange of even numbers of photons with the field.

Journal of the Optical Society of America B•Nov 1, 1985•32 citations

Atomic motion in resonant fluctuating laser radiation

R. J. Cook

The effect of field fluctuations on the motion of a two-level atom in resonant laser radiation is investigated theoretically. The internal motion of the atom is treated quantum mechanically (optical Bloch equations); the translational motion, which is coupled to the internal motion, is treated classically (Ehrenfest's theorem); and the fluctuating radiation is treated as a classical electromagnetic wave with stochastic phase (phase-diffusion model). An expression for the radiation force and equations of motion for the ensemble-averaged Bloch vector are derived and used to calculate (i) the radiation force in a plane running wave, (ii) the steady-state radiation force in a general standing wave, and (iii) the dissipative force in a plane standing wave in the limit of strong phase fluctuations. In case (iii) it is found that the atomic velocity is damped when the radiation is tuned above resonance, which is opposite to the case of a weak coherent standing wave, in which damping occurs for radiation tuned below resonance. It is shown that fluctuations have a substantial effect on the radiation force only when the spectral width of the radiation approaches or exceeds the spontaneous emission rate.

Physical Review A•Jan 1, 1980•26 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

Deflection of an atomic beam by a laser wave: transition between diffractive and diffusive regimes

Christian Tanguy, Serge Reynaud, Claude N. Cohen-Tannoudji

The exchange of momentum between atoms and photons in a deflection experiment is usually described by different formalisms depending on whether the interaction time T is shown or long compared with the radiative lifetime tau R . The authors present a new approach to this problem leading to a single theoretical expression valid in both limits and therefore allowing the transition between them to be studied. They interpret in this way the resonant Kapitza-Dirac effect and the optical Stern and Gerlach effect appearing in the short-time limit (T<< tau R ) as well as the deflection profiles usually deduced from a Fokker-Planck equation in the long-time limit (T>> tau R ). The transition between these two regimes is interpreted in terms of momentum transfer due to absorption and stimulated emission of laser photons, convoluted by the distribution of recoil due to spontaneously emitted photons.

Journal of Physics B Atomic and Molecular Physics•Dec 14, 1984•72 citations
Deflection of an atom due to momentum transfer from a strong resonant standing electromagnetic wave is investigated theoretically in the limit of short atom-field interaction time. The translational and internal motions of the atom are treated quantum mechanically, while the field is treated classically. It is shown that momentum transfer from a standing wave to an atom proceeds at the induced or Rabi rate, rather than the spontaneous rate characteristic of radiation pressure. In a typical case, atomic deflections of order 1\ifmmode^\circ\else\textdegree\fi{} are achieved with 106{10}^{6}106 W/cm2{\mathrm{cm}}^{2}cm2 field intensity in a time less than the natural lifetime of the excited atom.
A general theory of the motion of a two-level atom in a resonant or near-resonant electromagnetic wave of arbitrary amplitude and phase, including effects of radiative relaxation due to interaction with the quantized vacuum field, is developed from first principles. Particular emphasis is placed on the effects of quantum-mechanical fluctuations of the radiation force and on the associated diffusion of atomic momentum due to spontaneous and induced absorption and emission processes. Analytic results and numerical examples are presented for (1) the lower bound on the temperature achievable by radiation cooling in a standing wave tuned below resonance, (2) the heating rate in a strong resonant standing wave, (3) the maximum confinement time for an atom in a Gaussian radiation trap, (4) the deflection and spreading of an atomic beam transversely illuminated by a strong resonant running wave, and (5) the transverse cooling of an atomic beam by a strong running wave tuned below resonance.
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 have observed momentum transfer from a standing-wave light field to an atomic beam. The atomic beam is split symmetrically into two peaks whose separation increases with field strength. The short interaction time ensures that this deflection is due to induced forces; these are described using a semiclassical dressed-atom treatment, which gives good agreement with the data. In addition to the splitting, we have observed diffraction of the atomic beam due to the exchange of even numbers of photons with the field.
The effect of field fluctuations on the motion of a two-level atom in resonant laser radiation is investigated theoretically. The internal motion of the atom is treated quantum mechanically (optical Bloch equations); the translational motion, which is coupled to the internal motion, is treated classically (Ehrenfest's theorem); and the fluctuating radiation is treated as a classical electromagnetic wave with stochastic phase (phase-diffusion model). An expression for the radiation force and equations of motion for the ensemble-averaged Bloch vector are derived and used to calculate (i) the radiation force in a plane running wave, (ii) the steady-state radiation force in a general standing wave, and (iii) the dissipative force in a plane standing wave in the limit of strong phase fluctuations. In case (iii) it is found that the atomic velocity is damped when the radiation is tuned above resonance, which is opposite to the case of a weak coherent standing wave, in which damping occurs for radiation tuned below resonance. It is shown that fluctuations have a substantial effect on the radiation force only when the spectral width of the radiation approaches or exceeds the spontaneous emission rate.
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.
The exchange of momentum between atoms and photons in a deflection experiment is usually described by different formalisms depending on whether the interaction time T is shown or long compared with the radiative lifetime tau R . The authors present a new approach to this problem leading to a single theoretical expression valid in both limits and therefore allowing the transition between them to be studied. They interpret in this way the resonant Kapitza-Dirac effect and the optical Stern and Gerlach effect appearing in the short-time limit (T<< tau R ) as well as the deflection profiles usually deduced from a Fokker-Planck equation in the long-time limit (T>> tau R ). The transition between these two regimes is interpreted in terms of momentum transfer due to absorption and stimulated emission of laser photons, convoluted by the distribution of recoil due to spontaneously emitted photons.