We present a detailed theoretical description of a recently proposed atomic scanning microscope in a cavity QED setup [D. Yang et al., Phys. Rev. Lett. 120, 133601 (2018)]. The microscope continuously observes atomic densities with optical subwavelength resolution in a nondestructive way. The superresolution is achieved by engineering an internal atomic dark state with a sharp spatial variation of population of a ground level dispersively coupled to the cavity field. Thus, the atomic position encoded in the internal state is revealed as a phase shift of the light reflected from the cavity in a homodyne experiment. Our theoretical description of the microscope operation is based on the stochastic master equation describing the conditional time evolution of the atomic system under continuous observation as a competition between dynamics induced by the Hamiltonian of the system, decoherence effects due to atomic spontaneous decay, and the measurement backaction. Within our approach we relate the observed homodyne current with a local atomic density and discuss the emergence of a quantum nondemolition measurement regime allowing continuous observation of spatial densities of quantum motional eigenstates without measurement backaction in a single experimental run.
We present a detailed theoretical description of a recently proposed atomic scanning microscope in a cavity QED setup [D. Yang et al., Phys. Rev. Lett. 120, 133601 (2018)]. The microscope continuously observes atomic densities with optical subwavelength resolution in a nondestructive way. The superresolution is achieved by engineering an internal atomic dark state with a sharp spatial variation of population of a ground level dispersively coupled to the cavity field. Thus, the atomic position encoded in the internal state is revealed as a phase shift of the light reflected from the cavity in a homodyne experiment. Our theoretical description of the microscope operation is based on the stochastic master equation describing the conditional time evolution of the atomic system under continuous observation as a competition between dynamics induced by the Hamiltonian of the system, decoherence effects due to atomic spontaneous decay, and the measurement backaction. Within our approach we relate the observed homodyne current with a local atomic density and discuss the emergence of a quantum nondemolition measurement regime allowing continuous observation of spatial densities of quantum motional eigenstates without measurement backaction in a single experimental run.
We propose and analyze a scanning microscope to monitor "live" the quantum dynamics of cold atoms in a cavity QED setup. The microscope measures the atomic density with subwavelength resolution via dispersive couplings to a cavity and homodyne detection within the framework of continuous measurement theory. We analyze two modes of operation. First, for a fixed focal point the microscope records the wave packet dynamics of atoms with time resolution set by the cavity lifetime. Second, a spatial scan of the microscope acts to map out the spatial density of stationary quantum states. Remarkably, in the latter case, for a good cavity limit, the microscope becomes an effective quantum nondemolition device, such that the spatial distribution of motional eigenstates can be measured backaction free in single scans, as an emergent quantum nondemolition measurement.
We are interested in dynamics of quantum many-body systems under continuous observation, and its physical realizations involving cold atoms in lattices. In the present work we focus on continuous measurement of atomic currents in lattice models, including the Hubbard model. We describe a Cavity QED setup, where measurement of a homodyne current provides a faithful representation of the atomic current as a function of time. We employ the quantum optical description in terms of a diffusive stochastic Schr\"odinger equation to follow the time evolution of the atomic system conditional to observing a given homodyne current trajectory, thus accounting for the competition between the Hamiltonian evolution and measurement back action. As an illustration, we discuss minimal models of atomic dynamics and continuous current measurement on rings with synthetic gauge fields, involving both real space and synthetic dimension lattices (represented by internal atomic states). Finally, by ``not reading'' the current measurements the time evolution of the atomic system is governed by a master equation, where---depending on the microscopic details of our CQED setups---we effectively engineer a current coupling of our system to a quantum reservoir. This provides interesting scenarios of dissipative dynamics generating ``dark'' pure quantum many-body states.
This is a review of state-of-the-art theory and experiment of the motion of cold and ultracold atoms coupled to the radiation field within a high-finesse optical resonator in the dispersive regime of the atom-field interaction with small internal excitation. The optical dipole force on the atoms together with the backaction of atomic motion onto the light field gives rise to a complex nonlinear coupled dynamics. As the resonator constitutes an open driven and damped system, the dynamics is nonconservative and in general enables cooling and confining the motion of polarizable particles. In addition the emitted cavity field allows for real-time monitoring of the particle's position with minimal perturbation up to subwavelength accuracy. For many-body systems, the resonator field mediates controllable long-range atom-atom interactions, which set the stage for collective phenomena. Besides the correlated motion of distant particles, one finds critical behavior and nonequilibrium phase transitions between states of different atomic order in conjunction with superradiant light scattering. Quantum-degenerate gases inside optical resonators can be used to emulate optomechanics as well as novel quantum phases such as supersolids and spin glasses. Nonequilibrium quantum phase transitions as predicted by, e.g., the Dicke Hamiltonian can be controlled and explored in real time via monitoring the cavity field. In combination with optical lattices, the cavity field can be utilized for nondestructive probing Hubbard physics and tailoring long-range interactions for ultracold quantum systems.
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Previous work in cavity quantum electrodynamics has focused principally on achieving the condition of strong coupling, such that the single-photon Rabi frequency for one atom in a cavity dominates the rates associated with all forms of dissipation and dephasing. Although strong coupling was convincingly demonstrated in these experiments, the use of thermal atomic beams as a source of atoms invariably limited the intracavity dwell time of any given atom to values marginally longer than the system's characteristic dynamical timescales. Accordingly, the observation of single-atom effects in these experiments required integration over the transits of many successive atoms through the optical resonator. In such ensemble-averaged experiments, the quantitative effects of dissipation and measurement could always be understood from the perspective of Master Equation formalisms. By contrast, our most recent work has incorporated laser cooling techniques to accomplish a thousand-fold increase in the dwell time of individual atoms while maintaining conditions of strong coupling. With this extreme separation of timescales, the effects of individual atoms on the cavity transmission can clearly be resolved. Moreover, detailed information on each individual atom's spatial trajectory through the cavity can be inferred from the time-varying amplitude and phase of the transmitted light. Understanding the exact nature of such correlations in real laboratory measurements requires not only a careful characterization of excess technical noise, but also an in-depth study of how (and when) aspects of continuous quantum measurement theory should properly be applied. This thesis primarily contains a detailed description of an experiment in which we used broadband heterodyne spectroscopy to record the complete time-evolution of interaction energy between one atom and a high-finesse optical cavity, during individual scattering events of [...] duration. With a characteristic interaction energy scale [...], we achieve a shot-noise limited measurement sensitivity [...] over a bandwidth that covers the dominant rates of variation in [...]. I also include two brief studies in quantum measurement theory, which highlight the significance of the experimental work for continuing research on conditional quantum dynamics. The first investigates quantum limits to broadband measurement of position and force, and the second proposes a novel trajectory-based approach to quantum system identification.
Cavity quantum electrodynamics offers the possibility of observing and controlling the motion of a few or individual atoms, enabling the realization of various quantum technological tasks such as quantum enhanced metrology or quantum simulation of strongly correlated matter. A core limitation of these experiments lies in the mode structure of the cavity field, which is hard coded in the shape and geometry of the mirrors. As a result, most applications of cavity QED trade spatial resolution for enhanced sensitivity. Here, we propose and demonstrate a cavity-microscope device capable of controlling in space and time the coupling between atoms and light in a single-mode high-finesse cavity, reaching a spatial resolution an order of magnitude lower than the cavity-mode waist. This is achieved through local Floquet engineering of the atomic level structure, imprinting a corresponding atom-field coupling. We illustrate this capability by engineering micrometer-scale coupling, using cavity-assisted atomic measurements and optimization. Our system forms an optical device with a single optical axis, has the same footprint and complexity as a standard Fabry-Perot cavity or confocal lens pair, and can be used for any atomic species. This technique opens a wide range of perspectives, from ultrafast cavity-enhanced midcircuit readout to the quantum simulation of fully connected models of quantum matter such as the Sachdev-Ye-Kitaev model. Published by the American Physical Society 2024
A quantum-nondemolition method to measure the number of photons stored in a high-Q cavity, introduced by Brune et al. [Phys. Rev. Lett. 65, 976 (1990)], is described in detail. It is based on the detection of the dispersive phase shift produced by the field on the wave function of nonresonant atoms crossing the cavity. This shift can be measured by atomic interferometry, using the Ramsey separated-oscillatory-field method. The information acquired by detecting a sequence of atoms modifies the field step by step, until it eventually collapses into a Fock state. At the same time, the field phase undergoes a diffusive process as a result of the back action of the measurement on the photon-number conjugate variable. Once a Fock state has been generated, its evolution under weak perturbation can be continuously monitored, revealing quantum jumps between various photon numbers. When applied to an initial coherent field, the intermediate steps of the measuring sequence produce quantum superpositions of classical fields, known as ``Schr\"odinger cat states.'' Ways to prepare and detect these states in a cavity subjected to a weak relaxation process are discussed. The effects analyzed in this article could realistically be observed by using circular Rydberg atoms and very high-Q superconducting microwave cavities. The possibility of photon ``manipulation'' through nonresonant atom-field interactions opens a domain in cavity QED studies.