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arXiv:1410.7152 · Physical Review A

Application of the weak-measurement technique to study atom-vacuum interactions

M. Zhang, Shuqiang Zhu

Published Oct 19, 2015• 12 citations
arXivHTMLPDF

Abstract

Quantum weak measurement has attracted much interest recently [J. Dressel et al., Rev. Mod. Phys. 86, 307 (2014).] because it could amplify some weak signals and provide a technique to observe nonclassical phenomena. Here, we apply this technique to study the interaction between the free atoms and the vacuum in a cavity. Due to the gradient field in the vacuum cavity, the external orbital motions and the internal electronic states of atoms can be weakly coupled via the atom-field electric-dipole interaction. We show that, within the properly postselected internal states, the weak atom-vacuum interaction could generate a large change to the external motions of atoms due to the postselection-induced weak values.

DOI
10.1103/physreva.92.043825

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Quantum weak measurement has attracted much interest recently [J. Dressel et al., Rev. Mod. Phys. 86, 307 (2014).] because it could amplify some weak signals and provide a technique to observe nonclassical phenomena. Here, we apply this technique to study the interaction between the free atoms and the vacuum in a cavity. Due to the gradient field in the vacuum cavity, the external orbital motions and the internal electronic states of atoms can be weakly coupled via the atom-field electric-dipole interaction. We show that, within the properly postselected internal states, the weak atom-vacuum interaction could generate a large change to the external motions of atoms due to the postselection-induced weak values.
Quantum weak measurement attracts much interests recently [Rev. Mod. Phys. 86, 307 (2014)], as it could amplify some weak signals and provide a technique to observe the nonclassical phenomenons. Here, we apply this technique to study the interaction between the free atoms and the vacuum in a cavity. Due to the gradient field in the vacuum cavity, the external orbital motions and the internal electronic states of the atoms can be weakly coupled via the atom-field electric-dipole interaction. We show an interesting phenomenon that, within the properly post-selected internal states, the weak atom-vacuum interaction could generate a large change to the external motions of atoms.
Quantum weak measurement, measuring some observable quantities within the selected subensemble of the entire quantum ensemble, can produce many interesting results such as the superluminal phenomena. An outcome of such a measurement is the weak value which has been applied to amplify some weak signals of quantum interactions in lots of previous references. Here, we apply the weak measurement to the system of relativistic cold atoms. According to mass-energy equivalence, the internal energy of an atom will contribute its rest mass and consequently the external momentum of center of mass. This implies a weak coupling between the internal and external degrees of freedom of atoms moving in the free space. After a duration of this coupling, a weak value can be obtained by post-selecting an internal state of atoms. We show that the weak value can change the momentum uncertainty of atoms and consequently help us to experimentally measure the weak effects arising from mass-energy equivalence.
This paper reviews the work on cavity quantum electrodynamics of free atoms. In recent years, cavity experiments have also been conducted on a variety of solid-state systems resulting in many interesting applications, of which microlasers, photon bandgap structures and quantum dot structures in cavities are outstanding examples. Although these phenomena and systems are very interesting, discussion is limited here to free atoms and mostly single atoms because these systems exhibit clean quantum phenomena and are not disturbed by a variety of other effects. At the centre of our review is the work on the one-atom maser, but we also give a survey of the entire field, using free atoms in order to show the large variety of problems dealt with. The cavity interaction can be separated into two main regimes: the weak coupling in cavity or cavity-like structures with low quality factors Q and the strong coupling when high- Q cavities are involved. The weak coupling leads to modification of spontaneous transitions and level shifts, whereas the strong coupling enables one to observe a periodic exchange of photons between atoms and the radiation field. In this case, atoms and photons are entangled, this being the basis for a variety of phenomena observed, some of them leading to interesting applications in quantum information processing. The cavity experiments with free atoms reached a new domain with the advent of experiments in the visible spectral region. A review on recent achievements in this area is also given.
Schrödinger cat states, representing coherent superpositions of macroscopically distinguishable states, are indispensable nonclassical resources for continuous-variable quantum information processing. Existing generation protocols typically rely on strong nonlinear interactions, complicated control techniques, or engineered dissipation, posing challenges for experimental implementation. Here, we propose a simple measurement-based protocol for generating Schrödinger cat states in a cavity-QED system by combining coherent driving, dispersive atom--cavity interactions, and atomic postselection. The atom--cavity interaction establishes coherent correlations between the atomic and photonic degrees of freedom, while the subsequent atomic postselection projects the cavity field onto a non-Gaussian superposition state with pronounced Wigner negativity. Numerical simulations based on the Lindblad master equation show that the generated Schrödinger cat states remain robust against moderate cavity dissipation. Our results demonstrate that conditional atomic measurements provide an effective and experimentally accessible approach for preparing nonclassical cavity states without relying on strong optical nonlinearities or engineered dissipation.
Weak values as introduced by Aharonov, Albert, and Vaidman (AAV) are ensemble-average values for the results of weak measurements. They are interesting when the ensemble is preselected on a particular initial state and postselected on a particular final measurement result. It is shown that weak values arise naturally in quantum optics, as weak measurements occur whenever an open system is monitored (as by a photodetector). The quantum-trajectory theory is used to derive a generalization of AAV's formula to include (a) mixed initial conditions, (b) nonunitary evolution, (c) a generalized (nonprojective) final measurement, and (d) a non-back-action-evading weak measurement. This theory is applied to the recent cavity-QED experiment demonstrating wave particle duality [G. T. Foster, L. A. Orozco, H. M. Castro-Beltran, and H. J. Carmichael, Phys. Rev. Lett. 85, 3149 (2000)]. It is shown that the ``fractional-order'' correlation function measured in that experiment can be recast as a weak value in a form as simple as that introduced by AAV.
Cavity quantum electrodynamics (QED) in the strong-coupling regime provides the opportunity to monitor and control the dynamics of a simple quantum system. A single Cesium atom interacts strongly with single-photon fields in the mode of a high-finesse optical cavity. When the resulting coherent coupling rate dominates dissipation in the system, strong coupling is realized and the system displays distinctively quantum behavior. The coupling between atomic internal states and the quantized cavity field allows for diverse protocols in quantum state preparation, quantum communication, and quantum logic. However, the atom's external or motional state must also be taken into account. My research develops cavity QED in the limit where the coherent atom-field coupling dominates the atomic kinetic energy and thus significantly affects the atomic center-of-mass motion. In this regime, the interaction of the atom with the cavity field provides both a means of controlling atomic motion and a signal for detecting that motion in real time with high signal-to-noise. The sensing capability of the ``atom-cavity microscope" is exploited to trap single atoms with single-photon fields and to monitor their orbits in real time as they are bound in the cavity. Such real-time position sensing is the basis for a detailed strategy and ongoing experiment to actively stabilize select aspects of an atom's motion within the cavity. As the cavity-enabled position measurement approaches the standard quantum limit, this work begins to realize a quantum servo for atomic position and to address questions of optimal state estimation and state preparation. In combination with other progress in cavity QED, it furthers the goal of controlled atom-field interactions for quantum information science.