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Physical Review Letters

Rabi Oscillations Revival Induced by Time Reversal: A Test of Mesoscopic Quantum Coherence

Tristan Meunier, S. Gleyzes, Paolo Maioli, Alexia Auffèves, Gilles Nogues, M. Brune, J. M. Raimond, S. Haroche

Published Jan 3, 2005• 126 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.94.010401

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•Jan 1, 2005•0 citations
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.
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.
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.
We describe the blueprint of an experiment in which the decoherence of a mesoscopic superposition of radiation states (``Schr\"odinger cat'') becomes a reversible process. When the high QQQ cavity containing the Schr\"odinger cat is coupled to another resonator, the mesoscopic quantum coherence first decays rapidly, then exhibits sharp revivals with the period of the energy exchange between the two cavities. The interpretation of this experiment emphasizes the link between decoherence and complementarity and leads to an illuminating quantitative interpretation of the usual irreversible decoherence phenomenon.
We perform experiments with Rydberg atoms crossing one at a time a superconducting cavity containing a few microwave photons. The coupling between the atoms and the cavity field is either resonant or dispersive. In the resonant case, quantum Rabi oscillations induced by the vacuum or by a small coherent field are observed. These signals reveals in a striking way the quantization of the field. Quantum Rabi oscillations are also used to prepare Fock states of radiation, to transfer information or to produce entanglement between two successive atoms crossing the cavity. Dispersive atom–field coupling is used to prepare and probe coherent superpositions of field states with different phases (Schrödinger's cat states). The progressive decoherence of these states is observed. These experiments constitute fundamental tests of quantum theory and shed light on the transition from quantum to classical in mesoscopic systems.
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.