Cavity Quantum Electrodynamics Berman Pdf Download
Rayén Rundall
Rydberg atoms crossing one by one a high Q microwave cavity can be entangled to the field stored in this cavity, leading to fundamental tests in quantum physics. The amplitudes of the quantum states superpositions involved in the entangled states can be controlled and adjusted at will, realizing a kind of engineered entanglement at variance with the spontaneous entanglement achieved in photon cascade or down conversion experiments. The atomic coupling to the cavity field can be either resonant or dispersive. In the resonant case, entanglement results from the reversible quantum Rabi oscillation which coherently mixes atomic energy and photon number eigenstates. In the dispersive case, the atom and field undergo reciprocal frequency shifts, which produces phase dependent entanglement. By combining resonant and dispersive techniques, three or more atoms could be entangled together. The atom-cavity system is also ideal to entangle an atom to a mesoscopic coherent field made of several photons. Superpositions of coherent fields of the kind imagined by Schrdinger in his famous cat metaphor have been generated and studied. The decoherence of these states has been observed, providing new insight into the quantum-classical boundary. The generalization of these experiments to complex systems, involving more atoms, more photons and more cavities, is under way.
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The next-higher-lying doublet contains two quanta of energy and lacks a classical explanation12,21,22. The corresponding dressed states have been observed (together with a few higher-order states) in microwave cavity QED13,14,15 and even ion trapping, where phonons play the role of photons23. At optical frequencies, evidence for these states has indirectly been obtained in two-photon correlation experiments where the conditional response of the system on detection of an emitted photon is monitored16,24,25,26. These optical experiments observe the quantum fluctuations in dissipative cavity QED systems but operate away from a resonance to a higher-lying state. Direct spectroscopy using a two-colour technique to excite the second doublet step-wise has been attempted in a pioneering experiment with atomic beams22. An unambiguous signature of these states remained elusive owing to large fluctuations in the number of atoms traversing the cavity.
Using single trapped atoms, we exploit the anharmonicity of the energy-level spectrum to drive a multiphoton transition directly from the vacuum state to a specific higher-lying state. We observe the quantum character of our cavity QED field by measuring a photon flux, not a photon correlation. To explain our technique, we note that a two-state atom coupled to a single-mode light field has a discrete spectrum consisting of a ladder of dressed states, , with frequencies
Difference between the nonlinear response on the two-photon resonance and the linear single-photon response, together with the prediction from a quantum theory with an immobile atom (solid line). For reference, we also show the nonlinearity expected from the saturation of a two-state atom coupled to a classical field (optical bistability theory, dashed line).
For completeness, we also analysed the nonlinear theory of optical bistability16,17 and found that it is inconsistent with all of the measurements presented here, as shown with simulations (see Supplementary Information, Discussion and Figs S1,S2). Specifically, the bistability theory predicts a behaviour close to the one we obtained with the theory of coupled oscillators. Explained differently, according to bistability theory, we are operating on the lower branch, where the corresponding nonlinear response is small (dashed line in Fig. 4). Indeed, the reported nonlinearity occurs with an occupation probability of the atomic excited state of at most 0.07. This is what makes it radically different from and dominant over the standard saturation nonlinearity for a two-state atom.
We thank N. Syassen for early contributions. Partial support by the Bavarian PhD programme of excellence QCCC, the DFG research unit 635, the DFG cluster of excellence MAP and the EU project SCALA are gratefully acknowledged.
Recent advances in nanofabrication have enabled the development of structures that can manipulate and localize light into volumes below a cubic optical wavelength with storage times of thousands of optical cycles [1].
The emergence of such high quality nanophotonic structures has opened new opportunities for the study of light-matter interaction [2]. For example, as a result of the localization of light within such ultra-small volume nano-resonators, large optical intensities can be achieved with only a few photons coupled. Further, such a system also enables strong interaction between single atom-like quantum emitters (e.g. quantum dots, nitrogen vacancy centers in diamond, etc.) embedded within the cavity and single photons. Not only is the interaction between light and matter stronger in such a nanocavity, but system dynamics occurs on much faster time scales (as the light emission and absorption rates increase with reduction in the optical volumes). Moreover, nanophotonic structures can be constructed and integrated on chip by standard semiconductor microfabrication processes, and are fully scalable.
Such structures can be employed as a more practical testbed for fundamental experiments on light-matter interactions (the field referred to as the cavity quantum electrodynamics, or cavity QED). As opposed to the atomic-cavity QED platform [2] on which such experiments have been explored for the past 30 years, the use of a quantum dot-nanocavity platform enables a much smaller, on-chip, scalable system, which is also simpler, as it eliminates the need for atom trapping inside a resonator (e.g., quantum dots are already naturally trapped inside the nano-resonator material, such as GaAs [3-5]). In addition, as a result of the ultra-small optical volumes, the interaction strength between the quantum dot and the cavity field - described by the so called vacuum Rabi frequency - is in the range of several 10's of GHz - three orders of magnitude higher than for the atomic system. Therefore, everything happens much faster as well. The practicality and speed make these structures also interesting as a platform for a new generation of classical and quantum information processing devices.
For example, one of the key properties of the system consisting of a single quantum dot strongly coupled to a resonator is that the presence of the dot can completely modify the optical transmission through such structure, from transparent to opaque for an optical beam on the resonance [3]. This could be done at a rate proportional to the vacuum Rabi frequency (i.e., 10's of GHz for the quantum dot-nanocavity system [3], as opposed to MHz in the atom-cavity system [2]), opening the opportunity to build practical devices such as an optical modulator controlled with a single quantum dot [6], which could be operated with control energies below 1aJ - many orders of magnitude lower than conventional modulators or electrical interconnects in computers [7]. In addition to enabling the construction of a new generation of computers, where light is used to communicate signal between cores in a processor with much higher speed and efficiency, this approach also addresses an important energy problem: namely, electrical interconnects in computers of large data centers already consume a significant fraction of our electricity today, and more than that produced by solar cells [7].
In addition to the potential for improving the properties of conventional devices for optical communications and interconnects (such as lasers and modulators), quantum nanophotonics is a viable candidate for building circuits for quantum information processing which employ quantum mechanical properties of matter and light to transmit information securely or to perform certain computations more efficiently [11]. Applications of interest include quantum networks and repeaters (that would enable secure transmission of information over large distances) [12], as well as quantum simulators which would enable studies of complex physical processes by constructing systems exhibiting analogous behavior.
Although most of the experiments being done at the moment are at the level of a single device (single quantum emitter) or a few of them, many of the goals outlined here require interconnection of many such nodes. This certainly poses a number of technological challenges, but we can greatly benefit from the access to matured semiconductor micro-processing technologies in achieving this goal.
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