Ramsey interferometry with a two-level Tonks-Girardeau gas

Abstract

We propose a generalization of the Tonks-Girardeau model that describes a coherent gas of cold two-level Bosons which interact with two external fields in a Ramsey interferometer. They also interact among themselves by contact collisions with interchange of momentum and internal state. We study the corresponding Ramsey fringes and the quantum projection noise which, essentially unaffected by the interactions, remains that for ideal Bosons. The dual system of this gas, an ideal gas of two-level Fermions coupled by the interaction with the separated fields, produces the same fringes and noise fluctuations. The cases of time-separated and spatially-separated fields are studied. For spatially separated fields the fringes may be broadened slightly by increasing the number of particles, but only for large particle numbers far from present experiments with Tonks-Girardeau gases. The uncertainty in the determination of the atomic transition frequency diminishes, essentially with the inverse root of the particle number.

8 pages, 5 figures

References in corpus (21)

• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• On the Improvement of Frequency Stardards with Quantum Entanglement
• Regimes of quantum degeneracy in trapped 1D gases
• Atom-Atom Scattering Under Cylindrical Harmonic Confinement: Numerical and Analytical Studies of the Confinement Induced Resonance
• Stability and phase coherence of trapped 1D Bose gases
• Effect of cold collisions on spin coherence and resonance shifts in a magnetically trapped ultra-cold gas
• Fermion-Boson Duality of One-dimensional Quantum Particles with Generalized Contact Interaction
• Realizing Discontinuous Wave Functions with Renormalized Short-Range Potentials
• Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor
• Tuning the interactions of spin-polarized fermions using quasi-one-dimensional confinement
• Breakdown of time-dependent mean-field theory for a one-dimensional condensate of impenetrable bosons
• Theory of spinor Fermi and Bose gases in tight atom waveguides
• Effective interactions, Fermi-Bose duality, and ground states of ultracold atomic vapors in tight de Broglie waveguides
• Suppression of inhomogeneous broadening in rf spectroscopy of optically trapped atoms
• Using magnetic chip traps to study Tonks-Girardeau quantum gases
• Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model
• Ramsey interferometry with ultracold atoms
• Theory of a one-dimensional double-X atom interferometer
• Analysis of a Magnetically Trapped Atom Clock
• Control of Ultra-cold Inelastic Collisions by Feshbash Resonances and Quasi-One-Dimensional Confinement
• Stability of spinor Fermi gases in tight waveguides

Cited by in corpus (9)

• Shortcuts to adiabaticity
• Exact Solution of Strongly Interacting Quasi-One-Dimensional Spinor Bose Gases
• Nonlinear Ramsey interferometry with the Rosen-Zener pulses on a two-component Bose-Einstein condensate
• Magnetic ordering and quantum statistical effects in strongly repulsive Fermi-Fermi and Bose-Fermi mixtures
• Relation between quantum dwell times and flux-flux correlations
• Dwell-time distributions in quantum mechanics
• The weakening of fermionization of one dimensional spinor Bose gases induced by spin-exchange interaction
• Quantum motion effects in an ultracold-atom Mach-Zehnder interferometer
• Low velocity limits of cold atom clocks