We present a scheme in which we investigate the two-slit experiment and the the principle of complementarity. PACS: 03.65.Ud; 03.67.Mn; 32.80.-t; 42.50.-p Keywords: principle of complementarity, cavity QED. The investigation of the double slit experiment in which we have two micromaser cavities, each one associated with one of the slits, was proposed before by Scully and Walther in a series of very interesting articles where they investigate the principle of complementarity and the uncertainty principle [1, 2, 3] and they conclude that the principle of complementarity is more fundamental than the uncertainty principle. Recently we have published an article [4] where we have got the same conclusion. In this article we proceed with a further investigation of the subject studied in [4]. As in [4] first we are going to consider a screen with two slits SL1 (at ζ1) and SL2 (at ζ2) with two cavities C1 and C2 behind respectively each slit, through which fly Rydberg atoms of relatively long radiative lifetimes [5], and first prepared in coherent state |α〉1 and |α〉2 [3, 6] respectively and later we consider the cavities prepared in an even coherent state |+〉1 and an odd coherent state |−〉2 respectively, where | ±〉k = | α〉k ± | −α〉k (1) [7]. We also assume perfect microwave cavities, that is, we neglect effects due to decoherence. Let us consider a three-level lambda atom interacting with the electromagnetic field inside a cavity where the upper and the two degenerated lower states are |a〉, |b 〉 and |c 〉 respectively, and for which the |a 〉 ⇀ ↽ |c 〉 and |a 〉 ⇀ ↽ |b 〉 transitions are in the far from resonance interaction limit. The time evolution operator U(t) for the atom-field interaction in a cavity Ck is given by [8] U(τ) = −e iϕa † k ak |a〉〈a | + 1
We present a scheme in which we investigate the two-slit experiment and the the principle of complementarity. PACS: 03.65.Ud; 03.67.Mn; 32.80.-t; 42.50.-p Keywords: principle of complementarity, cavity QED. The investigation of the double slit experiment in which we have two micromaser cavities, each one associated with one of the slits, was proposed before by Scully and Walther in a series of very interesting articles where they investigate the principle of complementarity and the uncertainty principle [1, 2, 3] and they conclude that the principle of complementarity is more fundamental than the uncertainty principle. Recently we have published an article [4] where we have got the same conclusion. In this article we proceed with a further investigation of the subject studied in [4]. As in [4] first we are going to consider a screen with two slits SL1 (at ζ1) and SL2 (at ζ2) with two cavities C1 and C2 behind respectively each slit, through which fly Rydberg atoms of relatively long radiative lifetimes [5], and first prepared in coherent state |α〉1 and |α〉2 [3, 6] respectively and later we consider the cavities prepared in an even coherent state |+〉1 and an odd coherent state |−〉2 respectively, where | ±〉k = | α〉k ± | −α〉k (1) [7]. We also assume perfect microwave cavities, that is, we neglect effects due to decoherence. Let us consider a three-level lambda atom interacting with the electromagnetic field inside a cavity where the upper and the two degenerated lower states are |a〉, |b 〉 and |c 〉 respectively, and for which the |a 〉 ⇀ ↽ |c 〉 and |a 〉 ⇀ ↽ |b 〉 transitions are in the far from resonance interaction limit. The time evolution operator U(t) for the atom-field interaction in a cavity Ck is given by [8] U(τ) = −e iϕa † k ak |a〉〈a | + 1
In cavity-quantum-electrodynamics experiments, two-level Rydberg atoms and single-photon microwave fields can be seen as qubits. Quantum gates based on resonant and dispersive atom-field effects have been realized, which implement various kinds of conditional dynamics between these qubits. We have also studied the interaction between a single atom and coherent fields stored in the cavity. By progressively increasing the number of photons in these fields, we have explored various aspects of the quantum-classical boundary. We have realized a complementarity experiment demonstrating the continuous evolution of an apparatus from a quantum to a classical behaviour. We have also prepared 'Schrödinger-cat'-like states of the field made of a few photons, and observed their decoherence. We present a brief review of these experiments along with a proposal to study larger systems, i.e. coherent fields with more photons. Fundamental limits to the size of mesoscopic superpositions of field states in a cavity will be briefly discussed.
In this chapter, we discuss two more experimental realizations of quantum optical phenomena, namely the interaction of an effective two-level atom with a quantized electromagnetic field in a high Q microwave cavity, the subject usually referred to as cavity QED, or sometimes CQED, and in the quantized motion of a trapped ion. Strictly speaking, these experiments are not optical, but they do realize interactions of exactly the type that are of interest in quantum optics, namely the Jaynes–Cummings interaction between a two-level system (an atom) and a bosonic degree of freedom, a single-mode cavity field in the case of a microwave cavity, and a vibrational mode of the center-of-mass motion of a trapped ion, the quanta being phonons in this case. We shall begin with a description of the useful properties of the so-called Rydberg atoms that are used in the microwave CQED experiments, proceed to discuss some general considerations of the radiative behavior of atoms in cavities, the CQED realization of the Jaynes–Cummings model, and then discuss the use of the dispersive, highly off-resonant, version of the model to generate superpositions of coherent states, i.e. the Schrödinger cat states of the type discussed in Chapters 7 and 9 for traveling wave optical fields but this time for a microwave cavity field. Finally, we discuss the realization of the Jaynes–Cummings interaction in the vibrational motion of a trapped ion.
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.
We suggest two possible experiments to verify the mysterious passing of single photon through both the slits simultaneously. The first experiment aims to measure polarization of photons reaching the screen using polarization detectors fixed on the screen on both sides of the midway line made up of locus of points equidistant from both the slits and further using two types of synchronization setups. Again, using the same two types of synchronization setups, we suggest the second experiment which is based on a simple idea, justified by uncertainty principle. We suggest that we can distinguish between photons that have definitely gone through both the slits simultaneously and those other photons that have gone only through any single slit, either through the one on the left side or through the other on the right side, at a time. We fix in the second experiment photon detectors on the screen on both sides of the midway line made up of locus of points equidistant from both the slits. These experiments aim at achieving experimental confirmation for complementarity principle due to N. Bohr.
We present several schemes for preparing and detecting coherent superpositions of classically distinct states of the electromagnetic field in one or two high-Q cavities. These proposals are based on two-atom correlation measurements, to be performed on circular Rydberg atoms interacting dispersively with the cavity fields. Changing the time interval between the two detected atoms allows a monitoring of the decay of quantum coherence due to dissipation. \textcopyright{} 1996 The American Physical Society.
We review recent experiments in which Rydberg atoms interacting with microwave photons in a superconducting cavity are used to perform quantum information manipulations. We describe quantum phase gates using atoms and photons as "qubits", various engineered entanglement experiments involving up to three particles at a time and ideal non-destructive measurements of single photons. We also analyse an atomic interferometry experiment which illustrates the link between the notions of complementarity and entanglement. We finally recall previous experiments performed with the same set-up, in which we had generated and studied quantum superpositions of coherent fields with different phases, the so called "Schrödinger cat states" of the field. The decoherence of these states was experimentally studied. We conclude by discussing some of the perspectives opened by this line of research.