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European Quantum Electronics Conference (EQEC)

Single-Atom Interferometry

R. Huesmann, Chr. Balzer, Ph. W. Courteille, Werner Neuhauser, P. E. Toschek

Published Aug 24, 2005• 0 citations
Publisher

Abstract

The phase shift of the hyperfine Larmor precession of an individual ground-state ${}^{171}{\mathrm{Yb}}^{+}$ ion upon pulsed variation of the ambient magnetic field has been measured by microwave-optical double resonance interpreted in terms of Mach-Zehnder interferometry. Averaging over an ensemble of individual measurements, compared with measurements on an ensemble of ions, demonstrates quantum ergodicity. Even a single measurement yields (incomplete) phase information. Outside the peaks and dips of the interferogram, where ion probing is incompatible with ion preparation, the results of measurements are stochastic. This is demonstrated by laser exciting the ion on an $E2$ line.

DOI
10.1109/eqec.1998.715017

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The phase shift of the hyperfine Larmor precession of an individual ground-state 171Yb+{}^{171}{\mathrm{Yb}}^{+}171Yb+ ion upon pulsed variation of the ambient magnetic field has been measured by microwave-optical double resonance interpreted in terms of Mach-Zehnder interferometry. Averaging over an ensemble of individual measurements, compared with measurements on an ensemble of ions, demonstrates quantum ergodicity. Even a single measurement yields (incomplete) phase information. Outside the peaks and dips of the interferogram, where ion probing is incompatible with ion preparation, the results of measurements are stochastic. This is demonstrated by laser exciting the ion on an E2E2E2 line.
The phase shift of the hyperfine Larmor precession of an individual ground-state 171Yb+{}^{171}{\mathrm{Yb}}^{+}171Yb+ ion upon pulsed variation of the ambient magnetic field has been measured by microwave-optical double resonance interpreted in terms of Mach-Zehnder interferometry. Averaging over an ensemble of individual measurements, compared with measurements on an ensemble of ions, demonstrates quantum ergodicity. Even a single measurement yields (incomplete) phase information. Outside the peaks and dips of the interferogram, where ion probing is incompatible with ion preparation, the results of measurements are stochastic. This is demonstrated by laser exciting the ion on an E2E2E2 line.
The microwave-induced dynamics of the nuclear spin and the laser-induced dynamics of the centre-of-mass motion of individual ions have been studied: (i) The phase shift of the hyperfine Larmor precession of a ground-state 171Yb+ ion upon pulsed variation of the ambient magnetic field has been measured by microwave-optical double resonance interpreted in terms of Mach-Zehnder interferometry and quantum ergodicity. Even a single measurement yields (partial) phase information. At the extremes of the fringes, the results of measurements are deterministic where ion probing is compatible with ion preparation, as demonstrated by laser-exciting an ion on an E2 line. (ii) Excitation and de-excitation spectra of the E2 line S1/2−D5/2 of an individual trapped 138Ba+ ion show different first-order sidebands of radial and axial ion vibration in the trap, since the vibrational distribution in the excited D5/2 level is modified by the ion being reduced to this level in null observations of resonance light. Delayed sideband deexcitation eventually leaves the ion in the Fock state |n=1〉 (“stochastic cooling”). Sideband modulation is identified as stroboscopic detection of the light-induced nutation.
The ground-state hyperfine transitions of trapped clouds of 9Be+, 201Hg+, and 171Yb ions have been made control microwave oscillators.1-5 The frequency stability of these atomic clocks exceeds that of a primary Cs frequency standard in the short-term regime and that of a hydrogen maser for long times. Systematic perturbations derive from the members of the cloud being placed in an inhomogeneous field and showing residual motion. A single cold ion kept in the field node of an electrodynamic trap lacks these perturbations. The precise control of a standard frequency requires a narrow and weak transition whose resonance can be hardly detected by observation of the fluorescence on this line.
We have experimentally demonstrated a general method to perform high-precision refractive index spectrum measurement using phase-shifting interferometry in a phase-tunable Mach–Zehnder interferometer. We observed coherent amplification on the refractive spectrum, across the Lamb dips of ground hyperfine states in a Doppler-broadened Rb87 vapor. Most importantly, the spectrum still has a large signal-to-noise ratio when the probe power is in the dark light level under which the method using a single interferogram fails. This experimental scheme is efficient for refractive spectrum measurements and could be extended for 2D phase imaging. It provides many potential applications for optical phase measurements in linear, nonlinear, and quantum optics.
An atomic magnetometer, and a method for using same is disclosed. The method for measuring an ambient magnetic field uses an atomic magnetometer that has a probe light beam with a probe axis that probes a polarization vector of an atomic population confined within a vapor cell. The method employs one or more measurement cycles. In each measurement cycle, the polarization vector is prepared in an initial state via an optical pumping pulse. The vapor cell is then subjected to the ambient magnetic field, which results in rotation of the polarization vector by Larmor precession. Within the measurement cycle, at a point in time after the polarization vector has been prepared in the initial state, the ambient magnetic field rotates the direction of the polarization vector, and at least one measurement is made of a projection of the Larmor-rotated polarization vector onto the probe axis during or after application of a magnetic waveform.