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Physical Review Letters

Single-Atom Interferometry

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

Published Feb 22, 1999• 33 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: 10.1103/physrevlett.82.1611

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The phase shift of the hyperfine Larmor precession of an individual ground-state

{}^{171}{\mathrm{Yb}}^{+}

E2

line.

The phase shift of the hyperfine Larmor precession of an individual ground-state

{}^{171}{\mathrm{Yb}}^{+}

E2

line.

{N}_{T}

being the total number of atoms or photons. This gives (i) a phase-shift error confidence ${C}_{68%}=2.67∕{N}_{T}$ with (ii) a single interferometric measurement. Different input quantum states can achieve the Heisenberg scaling $\ensuremath{\sim}1∕{N}_{T}$ but with higher prefactors and at the price of a statistical analysis of two or more independent measurements.