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RabiOscillations Revival Induced byTimeReversal: ATestofMesoscopic Quantum Coherence

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

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

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.

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•Jan 1, 2005•0 citations
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.
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.
The interaction of circular Rydberg atoms with a high-quality microwave cavity makes it possible to realize complex quantum state manipulations. The state of an atom can be “copied” onto the cavity. Reversing this operation at a later time with a second atom, we realize an elementary “quantum memory” holding an atomic quantum coherence for a while in a cavity mode. We have also generated two-atom entangled states of the Einstein-Podolsky-Rosen type. At variance with previous experiments, this one implies massive particles in a completely controlled process. These entanglement manipulations can be generalized to more complex or to mesoscopic systems and open the way to new tests of fundamental aspects of the quantum world.
Cavity quantum electrodynamics (QED) has become one of themost successful tools for quantum information processing, butalso for the study of other pure quantum effects. In thisthesis we investigate one such system, the micromaser; an atomtraverse a cavity and interacts with the quantized modes of thecavity field. Today, the relaxation times of the atom and thecavity field can be made orders of magnitude longer than singleinteraction times, which makes it possible to carry out severaloperations on the system before decoherence becomessignificant. One can often, to a good approximation, treat themicromaser problem by considering the atom as a two-levelsystem interacting with just one of the modes, and losses ofthe combined system can be neglected during the interaction.Any rotations of the atomic Bloch vector during the interactionare, in principle, achievable with modern laser techniques. Forexample, the atom can be Stark shifted in a controlled fashionwith external lasers while it passes through the cavity.The micromaser is theoretically well described by the famousJaynes-Cummings model. Here we look into the problem arisingwhen the parameters of the Jaynes-Cummings model, which are theatom-field coupling and detuning, are allowed to vary in time.What possibilities may occur by letting the parameters dependon time? This question is fairly unanalyzed in the literatureand we are especially interested in preparing variousnon-classical states of the field. The states of the atoms aremeasured after the interactions with thefield and we considerboth the cases when the results of the detections are collectedor not. It is shown that, both in the non-selective andselective measurement procedure, any Fock state can begenerated. We also discuss how one can heat up or cool down thefield and how to prepare entangled states including more thanone mode. The photon field statistics are investigated when theparameters becomes time dependent and field losses areconsidered.
A single circular Rydberg atom is used to prepare in a high quality superconducting cavity a “Schrödinger cat” state, quantum superposition of two coherent fields with different classical phases. A second atom probes the cavity state after a tunable delay. The decay of the quantum correlations between the two atoms reveals the evolution of the field state from an initial quantum superposition into a mere statistical mixture. The time scale of this decay decreases when the separation between the two components increases. This is the first experimental observation of the dynamics of decoherence, lying at the heart of the quantum measurement process.
We present various schemes tomanipulate andstore quantumoptical fields into atomic ensembles andshowhowtorealize quantummemoryoperations, entangle atomic ensembles or teleport anatomic ensemble quantum state withhighefficiency. A major challenge inquantum information andcommunication lies intheability tomanipulate andstore quantum states ondemand. Quantum networks consisting ofatomic ensemble nodes connected bylight represent apromising, wayto achieve robust quantum communication. Because ofthelonglifetime oftheir ground state spin, atomic ensembles are goodcandidates tostore thequantum state ofoptical light fields. Wepropose ascheme toachieve quasi-perfect atom-field quantum state transfers inon-resonance Electromagnetically Induced Transparency (EIT) oroff-resonant Ramanconfigurations (11. Weshowthat dissipation isnegligible forsuch interactions, sothat thequantum states arepreserved during transfer operations. Wefirst showhowtomapabroadband squeezed vacuumontotheatomic ground state coherence ofaspin-polarized ensembles. Wefind theoptimal conditions forhighefficiency transfer andpresent amethod toreadout theatomic state inorder toperform aquantum memoryoperation (11. Wealso compare cavity andsingle passschemes; eventhough a cavity interaction turns outtobemoreefficient, single passinteraction should allow forverygoodquality transfer for realistic experimental parameters. We thenpropose toentangle twomacroscopic atomic ensembles using apairofEPR-correlated incident fields. Entanglement isalsoshowntobeconserved during on-resonant oroff-resonant interactions, andcanbestored fora longtimeintwospatially separated ensembles (2). Theatomic entanglement canthenbereadout intheoptical fields exiting thecavities.