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European Quantum Electronics Conference (EQEC)

Rabi oscillations revival induced by time reversal: a test of mesoscopic quantum coherence

S. Gleyzes, Christine Guerlin, Stefan Kuhr, Gilles Nogues, M. Brune, J. M. Raimond, S. Haroche

Published Jan 1, 2005• 3 citations
Publisher

Abstract

Using a technique reminiscent of the spin-echo, the paper reports on the demonstration of the coherent superposition of the two dephased fields. The atom is first interacted with the field. Collapse of the Rabi oscillations is then observed. The phase distribution is measured to check that the field has been split into two components. A /spl pi/-pulse is applied that swaps the two atomic states correlated to the phase components. This amounts to a time-reversal operation. The field components then reverse their evolution in the phase plane, until they merge back together. An induced Rabi revival is observed that proves the coherence of the whole process.

DOI
10.1109/eqec.2005.1567454

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Using a technique reminiscent of the spin-echo, the paper reports on the demonstration of the coherent superposition of the two dephased fields. The atom is first interacted with the field. Collapse of the Rabi oscillations is then observed. The phase distribution is measured to check that the field has been split into two components. A /spl pi/-pulse is applied that swaps the two atomic states correlated to the phase components. This amounts to a time-reversal operation. The field components then reverse their evolution in the phase plane, until they merge back together. An induced Rabi revival is observed that proves the coherence of the whole process.
Using an echo technique proposed by Morigi et al., we have time-reversed the atom-field interaction in a cavity quantum electrodynamics experiment. The collapse of the atomic Rabi oscillation in a coherent field is reversed, resulting in an induced revival signal. The amplitude of this "echo" is sensitive to nonunitary decoherence processes. Its observation demonstrates the existence of a mesoscopic quantum superposition of field states in the cavity between the collapse and the revival times.
Theresonant interaction ofatwolevel atomwith acoherent field isawell knownphenomenon inquantum optics. Inthecaseofamesoscopic field, theRabioscillations undergo acollapse, followed later byperiodic revivals. Thefield itself isalso modified bytheinteraction with theatom. Whenanatominteracts with amesoscopic coherent field, thephase ofthefield getsentangled withtheatomic state. Moreprecisely, thefield issplit into twophase components rotating slowly inopposite directions inphase space, eachcorrelated toanatomic state corresponding toa dipole inphase orir-out ofphase withthefield. Thefinal state oftheatom-field system isthus entangled. Ourexperiment usescircular Rydberg atomsinteracting with asuperconducting cavity. Inaprevious work[1], wehaveexperimentally observed that thefield issplit into twophase components bymeasuring thephase distribution after theinteraction. Now,using atechnique reminiscent ofthespin-echo, wehavebeenable todemonstrate that the superposition ofthese twodephased fields isindeed coherent [2]. Wefirst let theatominteract with thefield. We observe thecollapse oftheRabioscillations. We measure thephase distribution tocheck that thefield hasbeensplit into twocomponents. Wethenapply ait-pulse that swapsthetwoatomic states correlated tothephase components. This amounts toatime-reversal operation. Thefield components then reverse their evolution inthephase plane, until theymergebacktogether. We observe atthis timeaninduced Rabirevival that proves thecoherence ofthewhole process. Thisrevival isevidence ofthetransient generation ofamesoscopic quantum superposition state inthecavity. Onepromising perspective istomeasuredirectly theWigner function ofthissuperposition andtomonitor its progressive decoherence. Thisgoal sets verystringent requirements onthecavity quality factor. Wehavedeveloped a newgeneration ofsuperconducting mirrors, forwhich wehavemeasured aquality factor of4xl0A9, 10times higher than with previous cavities, opening awealth ofpossibilities forfundamental decoherence studies. Wearealso building anewset-up with twocavities, allowing ustogenerate entangled pairs ofphotons, toteleport atoms overlong distances oreventocreate anon-local mesoscopic quantum superposition.
The simple resonant Rabi oscillation of a two-level system in a single-mode coherent field reveals complex features at the mesoscopic scale, with oscillation collapses and revivals. Using slow circular Rydberg atoms interacting with a superconducting microwave cavity, we explore this phenomenon in an unprecedented range of interaction times and photon numbers. We demonstrate the efficient production of cat states, which are the quantum superposition of coherent components with nearly opposite phases and sizes in the range of few tens of photons. We measure cuts of their Wigner functions revealing their quantum coherence and observe their fast decoherence. This experiment opens promising perspectives for the rapid generation and manipulation of nonclassical states in cavity and circuit quantum electrodynamics.
Quantum Rabi oscillation in cavity quantum electrodynamics is at the very heart of the interaction of an atomic system with a single electromagnetic field in a resonator. It has proved a powerful tool to entangle the atom with the field in the case of an empty cavity (vacuum Rabi oscillation). On the other side, as soon as the field is macroscopic, its state seems unaffected and one observes the well-known phenomenon of classical Rabi oscillation which only affects the atomic populations. We propose to experimentally investigate the frontier between those two behaviours, when one has to take into account the fluctations of the photon number. In order to do so, we let interact circular Rydberg atoms with a microwave resonator in which a mesocopic field is injected (a few tens of photons). We observe a strong correlation between specific atomic states and the phase of the injected field, which is measured by a homodyne technique. Those correlations explain in an easy way all the standard features of quantum Rabi oscillations (especially the collapses and revivals). Moreover they allow for the preparation of atom-field entangled state as well as non classical Schroedinger cat like states for the field.
Time-domain observations of coherent oscillations between quantum states in mesoscopic superconducting systems have so far been restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a method for direct observation of Rabi oscillations in a phase qubit. The external source, typically in the GHz range, induces transitions between the qubit levels. The resulting Rabi oscillations of supercurrent in the qubit loop are detected by a high-quality resonant tank circuit, inductively coupled to the phase qubit. Here we present the results of detailed computer simulations of the interaction of a classical object (resonant tank circuit) with a quantum object (phase qubit), which explicitly account for the back action of a tank circuit. According to the results of our simulations the Rabi oscillations in the MHz range can be detected using the conventional NMR pulse Fourier technique.