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Exploring the quantum world with photons trapped in cavities and Rydberg atoms

J. M. Raimond

Published Jun 12, 2014• 3 citations
Publisher

Abstract

Abstract This chapter presents a review of the latest achievements in cavity quantum electrodynamics with Rydberg atoms. In particular, it illustrates an example of quantum feedback, which is the stabilization of a Fock state in the cavity against spontaneous emission. The feedback process involves the rapid measurement of atoms passing through the cavity and performing a quantum nondemolition measurement of its photon number. The information is fed to a processor that in real time computes the right classical signal to send to the cavity to re-pump it in the right way.

DOI
10.1093/acprof:oso/9780199681181.003.0011

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Fock states with photon numbers n up to 7 are prepared on demand in a microwave superconducting cavity by a quantum feedback procedure that reverses decoherence-induced quantum jumps. Circular Rydberg atoms are used as quantum nondemolition sensors or as single-photon emitter or absorber actuators. The quantum nature of these actuators matches the correction of single-photon quantum jumps due to relaxation. The flexibility of this method is suited to the generation of arbitrary sequences of Fock states.

arXiv:1203.1920•Physical Review Letters•Jun 15, 2012•126 citations
Abstract This chapter presents a review of the latest achievements in cavity quantum electrodynamics with Rydberg atoms. In particular, it illustrates an example of quantum feedback, which is the stabilization of a Fock state in the cavity against spontaneous emission. The feedback process involves the rapid measurement of atoms passing through the cavity and performing a quantum nondemolition measurement of its photon number. The information is fed to a processor that in real time computes the right classical signal to send to the cavity to re-pump it in the right way.
The ubiquitous decoherence phenomenon is responsible for the lack of quantum superpositions at the macroscopic scale. It is increasingly difficult to isolate a quantum system from its environment when its size increases. Making use of the weird quantum properties of mesoscopic quantum states thus requires efficient means to combat decoherence. One option is real-time quantum feedback. It features the components of a conventional feedback: measurement of the system's state (sensor), analysis (controller), and feedback action (actuator) aiming to the target state. The random back-action of the measurements by the sensor makes quantum feedback much more difficult than its classical counterpart. Mesoscopic photon number (Fock) states feature a decoherence rate proportional to the photon number. They are thus a simple example of a fragile quantum resource. We demonstrated recently two quantum feedback schemes continuously stabilizing Fock state of a microwave field in a high-quality cavity. Sensitive atoms, crossing the field one at a time, are used as quantum nondemolition (QND) probes of its photon number. The feedback actuator is either a classical source [Sayrin et al., Nature (London) 477, 73 (2011)] or individual resonant atoms emitting or absorbing one photon each [Zhou et al., Phys. Rev. Lett. 108, 243602 (2012)]. Both schemes detect the quantum jumps of the photon number and efficiently correct their adverse effects, preparing and preserving a fragile quantum resource. We present an in-depth analysis of our methods, which sheds light onto the fundamental difficulties encountered in quantum feedback, in particular concerning the state estimation algorithm, and onto the ways to circumvent them. These results open the way to informationally optimal QND measurements or to the stabilization of mesoscopic field state superpositions. More generally, they can be cast in a variety of contexts to loosen the tight constraints set by decoherence in quantum metrology and quantum information processing.
After a brief review of experiments realized on optical fields, the author will focus on recent cavity quantum electrodynamics (cavity QED) studies performed on a microwave field trapped between highly reflecting superconducting mirrors and probed by Rydberg atoms. Exotic Fock and Schrodinger cat states of radiation are generated, kept in a cavity for an observable time and reconstructed in details. The decoherence of these states - i.e. their progressive transformation into mundane classical states under the effect of their coupling to the environment - is recorded in real time, realizing a detailed exploration of the quantum to classical boundary.
We propose a quantum feedback scheme for the preparation and protection of photon-number states of light trapped in a high-QQQ microwave cavity. A quantum nondemolition measurement of the cavity field provides information on the photon-number distribution. The feedback loop is closed by injecting into the cavity a coherent pulse adjusted to increase the probability of the target photon number. The efficiency and reliability of the closed-loop state stabilization is assessed by quantum Monte Carlo simulations. We show that, in realistic experimental conditions, the Fock states are efficiently produced and protected against decoherence.
A single two-level emitter coupled to a single mode of an electromagnetic resonator constitutes the most fundamental instance of light--matter interaction. Realizations of this type of system are investigated in the field of cavity quantum electrodynamics (cavity QED). Particularly important are schemes in which the coupling is strong enough to exceed the spontaneous emission rate as well as cavity damping. In this case, the coherent exchange of excitation between source and photon is the dominating process, providing the unique possibility to deterministically control the quantum evolution of the system. Great progress has recently been accomplished, technologically as well as conceptually, and the focus section in this issue of Journal of Optics B: Quantum and Semiclassical Optics features five articles highlighting important recent developments in the field. Strong coupling between single atoms and the electromagnetic cavity field have been achieved in two distinct regimes, the optical and the microwave region. The latter is represented by the micromaser, a high-Q microwave cavity pumped by a beam of highly excited Rydberg atoms. It has proved to be an almost ideal system for the generation of non-classical field states. A constraint in these experiments is the fact that the field inside the cavity can only be examined indirectly, by analysing the occupation of atoms leaving the cavity. While only two atomic states were previously identified for this purpose, V A Reshetov shows in his article (pages 119--126) that more information on the field may be extracted by taking advantage of the Zeeman substructure of the atomic levels. In the optical domain of cavity QED, by contrast, the state of the resonator field may be probed directly by measuring the light leaking from the cavity using photodetectors. In order to minimize damping, high-quality cavities must be employed. In most optical experiments these are Fabry--Perot resonators with ultra-high reflectivity mirrors, with losses as low as a few parts per million being state of the art. At the same time, the coupling of atoms and photons is enhanced by reducing the length of the cavity, so that strong coupling conditions are reached. A very attractive application of this type of cavity QED setup is the possibility of exerting control over the quantum dynamics of the system. An impressive example is the implementation of quantum feedback, reported in the paper by W P Smith and L A Orozco (pages 127--134). Using information gained from detecting a single photon escaping from the cavity, active feedback is applied to halt the dynamical evolution of the system. This is the first time active feedback has been used to modify the quantum evolution of a system at the single-photon level. The authors discuss how detunings between the subsystems affect the quantum feedback, an issue particularly relevant for ensembles of atoms with a spread in detuning. Perfect quantum feedback in this case requires the use of additional parameters to control the system. The majority of optical cavity QED experiments performed so far have used as a medium atoms traversing the cavity on random trajectories, such as, for example, thermal atomic beams. In this case, the observation of quantum effects is degraded in two ways. The Doppler effect and the finite transit time lead to line broadening, while the spatial structure of the cavity mode results in atoms in different locations experiencing different coupling with the photonic field. J E Reiner et al (pages 135--142) investigate the impact of these effects on quantum fluctuations in their cavity QED system. In order to overcome line broadening, they have developed a continuous cold atomic beam, extracted from a magneto-optical trap. An even better control of broadening effects and fluctuating coupling strength is provided by trapping the atoms inside the cavity and cooling them to temperatures at which their position spread is smaller than the optical wavelength. Much recent activity has been devoted to developing such an ultimate cavity QED system. A Vukics et al (pages 143--153) present a theoretical proposal for dynamically trapping and cooling atoms inside a cavity. By driving the atoms with a standing wave injected from the side of the cavity and by weakly exciting the cavity field itself, they predict three-dimensional trapping of the atom for periods around 1 second, an extremely long time on the typical scale of cavity QED dynamics. The essential component of their scheme is the interference between the two driving fields, determining the temperature of the particle and the stable trapping positions. In the quest for better confinement of radiation, lately, an appealing alternative to the Fabry--Perot cavity has been investigated -- the optical microsphere resonator. A sphere with a diameter of a few tens of microns, it supports so-called whispering gallery modes near its circumference, for which quality factors up to 10 10 have been measured. In order to exploit the correspondingly low field damping rates for cavity QED, a method must be found to couple atomic or solid state emitters to these modes. S Göotzinger et al (pages 154--158) report the coupling of single nanocrystals on the surface of a microsphere through the evanescent field of the mode. Selective excitation of a single nano-emitter was accomplished with a scanning confocal microscope. The system is a promising candidate for cavity QED with single-quantum emitters. The ability to fully control the quantum dynamics of atoms and light is beginning to spawn early applications. The most notable example is quantum information processing. This requires the coherent manipulation of single-quantum systems, which is ideally provided by cavity QED interaction in the strong-coupling limit. The development of practical devices will be among the principal future tasks for research in the field. This will include physical systems, which have not been covered in this issue, such as semiconductors, quantum dots as emitters, or photonic crystals as resonator structures. Cavity QED is therefore guaranteed to remain a vigorous field in the years to come.
Fock states with photon numbers n up to 7 are prepared on demand in a microwave superconducting cavity by a quantum feedback procedure that reverses decoherence-induced quantum jumps. Circular Rydberg atoms are used as quantum nondemolition sensors or as single-photon emitter or absorber actuators. The quantum nature of these actuators matches the correction of single-photon quantum jumps due to relaxation. The flexibility of this method is suited to the generation of arbitrary sequences of Fock states.