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

Coherent squeezed states of motion in an ion trap generated with Raman-driven sideband transitions

Heping Zeng, Fucheng Lin

Published Jul 1, 1995• 29 citations
Publisher

Abstract

Raman interaction between two internal levels and its sideband cooling of a trapped ion or atom are investigated in copropagating traveling-wave light fields for localization beyond the Lamb-Dicke limit. Under certain conditions, only the first-order sideband excitations (\ensuremath{\Vert}n〉\ensuremath{\rightarrow}\ensuremath{\Vert}n\ifmmode\pm\else\textpm\fi{}1〉 with \ensuremath{\Vert}n〉 being a Fock state) may play a significant role. This provides an experimental realization of the Jaynes-Cummings model with quantized center-of-mass motion beyond the Lamb-Dicke regime, which can be used to measure the statistics of the quantized motion, and thus to detect nonclassical states of motion. Moreover, the multichromatic two-photon Raman excitations of the trapped particle can be used for the preparation of coherent squeezed states of motion.

DOI
10.1103/physreva.52.809

Related papers

Nonlinear Raman vibrational excitation of a trapped ion

Heping Zeng, Yuzhu Wang, Yusaburo Segawa

Raman sideband excitations driven by counterpropagating Raman beams are analyzed for the trapped ion under the localization conditions in and beyond the Lamb-Dicke regime. Multiquantum vibrational couplings are demonstrated to produce significant effects on the Raman sideband transitions and the relevant Raman excitations of the trapped ion beyond the Lamb-Dicke regime. The quantum features of the vibrational states attained by exciting the motional ground state are closely associated with the nonlinear vibronic couplings, Raman excitation, and localization conditions. Quantum entanglement and quantum interference are discussed for the trapped ion under various Raman excitation and localization conditions. The results are compared with the recent experiments. Further experimental attempts are proposed to use the single trapped ${}^{25}{\mathrm{Mg}}^{+}$ ion in a linear ion trap.

Physical Review A•Mar 1, 1999•10 citations

Motional displacement and entanglement of a trapped ion

Heping Zeng, Yuzhu Wang, Yusaburo Segawa

The first sideband Raman excitations driven by counter-propagating Raman beams are analysed for the trapped ion under the localization condition in or beyond the Lamb-Dicke regime. It is demonstrated that multiquantum processes in the vibrational couplings produce significant effects on the the first sideband Raman transitions and the relevant Raman displacements for the trapped ion beyond the Lamb-Dicke regime. The quantum features of the vibrational states attained by displacing the motional ground state are demonstrated to be closely associated with the nonlinear vibronic couplings. Quantum entanglement, and quantum interference as well, are discussed for ion traps with various Raman excitation and localization conditions. The results are compared with the recent experiment reported by Monroe C et al in 1996 Science 272 1131-5.

Journal of Physics B Atomic Molecular and Optical Physics•Jan 1, 1999•0 citations

Raman sideband transitions and quantum manipulating vibrational motion of a trapped ion

Heping Zeng, Fei Lin

It is well known that electronic transitions driven by nearly resonant travelling- or standing- wave lasers are often accompanied with vibrational sideband transitions of a single trapped ion undergoing quantized center-of-mass motion [1], Our previous studies showed that quantum statistics of radiation fields can be used to manipulate the vibronic motion of a trapped ion localised within the Lamb-Dicke limit (LDL) [2]. The present paper addresses quantum manipulating vibronic motion of an ion trapped far beyond the LDL.

•Jul 14, 1996•0 citations

Preparation of Fock states and squeezed states of motion in ion traps

J. I. Cirac, R. Blatt, A. S. Parkins +1 more

(1) A technique for the preparation of Fock states of a harmonic oscillator strongly coupled to a single two-level atomic transition is proposed due to the observation of quantum jumps. Examples are taken from the fields of ion trapping and cavity QED, where number states of he quantized atomic motion and photon number states may be prepared respectively. (2) We discuss a scheme for preparing coherent squeezed states of motion in an ion trap based on the multichromatic excitation of a trapped ion by standing- and traveling-wave light fields. The squeezed state is produced when the beat frequency between two standing-wave light fields is equal to twice the trap frequency, and is indicated by a {open_quotes}dark resonance{close_quotes} in the fluorescence emitted by the ion.

Bulletin of the American Physical Society•May 1, 1993•0 citations

Cooling of a trapped ion in the strong-sideband regime

C. A. Blockley, Daniel F. Walls

A single two-level atom, with quantized center-of-mass motion, is constrained to move in a one-dimensional harmonic potential while interacting with a single-mode classical traveling-wave light field. When the classical light field is tuned to the atom's lower vibrational sideband, cooling can occur. The strong-sideband and Lamb-Dicke perturbation regimes for the system are defined. The steady-state and time-evolution behaviors in the strong-sideband regime are discussed and, in particular, it is shown that the steady-state average trap number saturates when spontaneous emission is weak and that the steady-state average trap number depends more strongly on the trap frequency in the saturated regime than previously predicted. Finally, the possibility of observing quantum jumps between trap levels is discussed.

Physical Review A•Mar 1, 1993•40 citations

Nonclassical vibrational states in a quantized trap

Heping Zeng, Fucheng Lin

The quantized center-of-mass (c.m.) motions of a single two-level atom or ion confined into a one-dimensional harmonic potential and interacting with a single-mode classical traveling-wave laser field are examined. We demonstrate that trap quantum states with remarkable nonclassical properties such as quadrature and amplitude-squared squeezing and sub-Poissonian statistics can be generated in this simple trap model when the c.m. motion is initially in certain coherent trap states. Our analyses also indicate that there exist some time regions where the production of nonclassical vibrational states is possible even if squeezing or sub-Poissonian statistics do not appear.

Physical Review A•Sep 1, 1993•16 citations
Raman interaction between two internal levels and its sideband cooling of a trapped ion or atom are investigated in copropagating traveling-wave light fields for localization beyond the Lamb-Dicke limit. Under certain conditions, only the first-order sideband excitations (\ensuremath{\Vert}n〉\ensuremath{\rightarrow}\ensuremath{\Vert}n\ifmmode\pm\else\textpm\fi{}1〉 with \ensuremath{\Vert}n〉 being a Fock state) may play a significant role. This provides an experimental realization of the Jaynes-Cummings model with quantized center-of-mass motion beyond the Lamb-Dicke regime, which can be used to measure the statistics of the quantized motion, and thus to detect nonclassical states of motion. Moreover, the multichromatic two-photon Raman excitations of the trapped particle can be used for the preparation of coherent squeezed states of motion.
Raman sideband excitations driven by counterpropagating Raman beams are analyzed for the trapped ion under the localization conditions in and beyond the Lamb-Dicke regime. Multiquantum vibrational couplings are demonstrated to produce significant effects on the Raman sideband transitions and the relevant Raman excitations of the trapped ion beyond the Lamb-Dicke regime. The quantum features of the vibrational states attained by exciting the motional ground state are closely associated with the nonlinear vibronic couplings, Raman excitation, and localization conditions. Quantum entanglement and quantum interference are discussed for the trapped ion under various Raman excitation and localization conditions. The results are compared with the recent experiments. Further experimental attempts are proposed to use the single trapped 25Mg+{}^{25}{\mathrm{Mg}}^{+}25Mg+ ion in a linear ion trap.
The first sideband Raman excitations driven by counter-propagating Raman beams are analysed for the trapped ion under the localization condition in or beyond the Lamb-Dicke regime. It is demonstrated that multiquantum processes in the vibrational couplings produce significant effects on the the first sideband Raman transitions and the relevant Raman displacements for the trapped ion beyond the Lamb-Dicke regime. The quantum features of the vibrational states attained by displacing the motional ground state are demonstrated to be closely associated with the nonlinear vibronic couplings. Quantum entanglement, and quantum interference as well, are discussed for ion traps with various Raman excitation and localization conditions. The results are compared with the recent experiment reported by Monroe C et al in 1996 Science 272 1131-5.
It is well known that electronic transitions driven by nearly resonant travelling- or standing- wave lasers are often accompanied with vibrational sideband transitions of a single trapped ion undergoing quantized center-of-mass motion [1], Our previous studies showed that quantum statistics of radiation fields can be used to manipulate the vibronic motion of a trapped ion localised within the Lamb-Dicke limit (LDL) [2]. The present paper addresses quantum manipulating vibronic motion of an ion trapped far beyond the LDL.
(1) A technique for the preparation of Fock states of a harmonic oscillator strongly coupled to a single two-level atomic transition is proposed due to the observation of quantum jumps. Examples are taken from the fields of ion trapping and cavity QED, where number states of he quantized atomic motion and photon number states may be prepared respectively. (2) We discuss a scheme for preparing coherent squeezed states of motion in an ion trap based on the multichromatic excitation of a trapped ion by standing- and traveling-wave light fields. The squeezed state is produced when the beat frequency between two standing-wave light fields is equal to twice the trap frequency, and is indicated by a {open_quotes}dark resonance{close_quotes} in the fluorescence emitted by the ion.
A single two-level atom, with quantized center-of-mass motion, is constrained to move in a one-dimensional harmonic potential while interacting with a single-mode classical traveling-wave light field. When the classical light field is tuned to the atom's lower vibrational sideband, cooling can occur. The strong-sideband and Lamb-Dicke perturbation regimes for the system are defined. The steady-state and time-evolution behaviors in the strong-sideband regime are discussed and, in particular, it is shown that the steady-state average trap number saturates when spontaneous emission is weak and that the steady-state average trap number depends more strongly on the trap frequency in the saturated regime than previously predicted. Finally, the possibility of observing quantum jumps between trap levels is discussed.
The quantized center-of-mass (c.m.) motions of a single two-level atom or ion confined into a one-dimensional harmonic potential and interacting with a single-mode classical traveling-wave laser field are examined. We demonstrate that trap quantum states with remarkable nonclassical properties such as quadrature and amplitude-squared squeezing and sub-Poissonian statistics can be generated in this simple trap model when the c.m. motion is initially in certain coherent trap states. Our analyses also indicate that there exist some time regions where the production of nonclassical vibrational states is possible even if squeezing or sub-Poissonian statistics do not appear.