Motional frequency shifts of trapped ions in the Lamb-Dicke regime

Abstract

First order Doppler effects are usually ignored in laser driven trapped ions when the recoil frequency is much smaller than the trapping frequency (Lamb-Dicke regime). This means that the central, carrier excitation band is supposed to be unaffected by vibronic transitions in which the vibrational number changes. While this is strictly true in the Lamb-Dicke limit (infinitely tight confinement), the vibronic transitions do play a role in the Lamb-Dicke regime. In this paper we quantify the asymptotic behaviour of their effect with respect to the Lamb-Dicke parameter. In particular, we give analytical expressions for the frequency shift, ``pulling'' or ``pushing'', produced in the carrier absorption band by the vibronic transitions both for Rabi and Ramsey schemes. This shift is shown to be independent of the initial vibrational state.

arXiv comment9 pages, 6 figures

References in corpus (11)

• Absolute Frequency Measurements of the Hg^+ and Ca Optical Clock Transitions with a Femtosecond Laser
• Recoil-free spectroscopy of neutral Sr atoms in the Lamb-Dicke regime
• Fast quantum gates for cold trapped ions
• Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor
• An accurate optical lattice clock with 87Sr atoms
• A high-accuracy optical clock via three-level coherence in neutral bosonic ${}^{88}$Sr
• Evaluation of the ultimate performances of a Ca+ single-ion frequency standard
• Long-time-scale revivals in ion traps
• Evolution of the N ion Jaynes-Cummings model beyond the standard rotating wave approximation
• Vibronic "Rabi resonances" in harmonic and hard-wall ion-traps for arbitrary laser intensity and detuning
• Transversal laser excitation of atoms in a waveguide

Cited by in corpus (6)

• Evidence for Nonlinear Isotope Shift in Yb${}^{+}$ Search for New Boson
• Part-per-billion measurement of the $4^2{S}_{1/2}\to 3^2{D}_{5/2}$ electric quadrupole transition isotope shifts between ${}^{42,44,48}$Ca${}^{+}$ and ${}^{40}$Ca${}^{+}$
• Vibrational Bloch-Siegert effect in trapped ions
• Avoided crossing resonances: structural and dynamical aspects
• The weakening of fermionization of one dimensional spinor Bose gases induced by spin-exchange interaction
• Low velocity limits of cold atom clocks