We have measured by Ramsey interferometry the dispersive light shifts produced on circular Rydberg states by very weak nonresonant microwave fields in a single cavity mode. This experiment yields an absolute measurement of mean photon numbers with a sensitivity of 0.1. The vacuum induced Lamb shift, equal to the light shift of ``half a photon,'' has been observed, providing a direct and absolute measurement of the zero-point field fluctuations in a cavity mode.
We have measured by Ramsey interferometry the dispersive light shifts produced on circular Rydberg states by very weak nonresonant microwave fields in a single cavity mode. This experiment yields an absolute measurement of mean photon numbers with a sensitivity of 0.1. The vacuum induced Lamb shift, equal to the light shift of ``half a photon,'' has been observed, providing a direct and absolute measurement of the zero-point field fluctuations in a cavity mode.
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.
Long lived circular Rydberg atoms interacting with high finesse superconducting cavities offer unique opportunities to perform tests on fundamental quantum mechanics. “Schrödinger cats”, multiparticle nonlocal correlations, “quantum teleportation” offer striking illustrations of the less intuitive aspects of quantum mechanics. At the heart of these experiments is the dispersive atom‐cavity interaction. We present its experimental manifestations, with the measurement of single photons light shifts and of Lamb shifts due to a single, empty, cavity mode. We then describe some possible extensions of this experiment, some of which being under way in our laboratory.
Circular Rydberg atoms, detected by the very sensitive and state selective field ionization method, can be used to measure and manipulate quantum fields stored in a cavity. The method is based on an interferometric detection of the dispersive energy shifts experienced by these atoms when they interact with a slightly off‐resonant field mode sustained by a cavity which the atoms cross one at a time. These shifts give rise to a translation of the Ramsey fringe pattern observed in the field ionization signal of the atoms. The method consitutes a non‐destructive way of photon counting. In this experiment, non local correlations between the atom and the cavity field are created, which could be used to perform new types of Einstein‐Podolsky‐Rosen experiments. Non classical fields could also be generated, which would display some of the properties discussed by Schrödinger in his famous ‘‘cat paradox.’’ We present the theory of these experiments which until very recently would have been considered as mere ‘‘gedanken’’ ones and we describe the operation of a Rydberg atom interferometer which has already enabled us to detect subphoton fields and to measure vacuum field effects in a cavity.
The coupling of atoms to high Q cavities results in strong modifications of the field and atomic frequencies. These effects are most conveniently analyzed in the ‘‘dressed atom’’ point of view. The vacuum Rabi splitting of the atom‐cavity resonance lines is now being observed in optical and microwave experiments where small samples of atoms resonantly interact with an empty cavity mode. Observation of this effect on a single atom coupled to a cavity vacuum is a realistic goal for experiments. Similar shifts are expected when the cavity mode is weakly excited. The detection of these shifts appears very promising for Quantum nondemolition measurements of very small photon numbers. We propose an experiment in which a microwave field stored in a high Q cavity is continuously monitored with the help of a non‐resonant beam of slow circular Rydberg atoms and we discuss possible applications of this method.
In the last decades the interest in studying interactions of Rydberg atoms or ensembles thereof with electromagnetic fields at optical and microwave frequencies has steadily increased. The physics Nobel prize of 2012, for instance, has been partially awarded to cavity quantum electrodynamics (QED) experiments with single Rydberg atoms that allow for quantum nondemolition measurements of the photon number in a superconducting microwave cavity. These experiments detect the dispersive shift of the atomic transition frequency that results from the interaction with the photons to measure the photon number nondestructively. In this thesis, we employ the reversed effect, the dispersive shift of the resonance frequency of the TE301 mode of a rectangular microwave cavity induced an ensemble of helium Rydberg atoms, to perform nondestructive measurements of the atom number. In a first experiment, we measure the dispersive interaction between a few thousand atoms in the 36s singlet state and a copper cavity with a quality factor of about Q = 5 · 10^3. We detect the dispersive shift by continuously measuring the changes in cavity transmission with a weak coherent probe tone that injects a few hundred photons into the cavity. We model the observed time dependence of the dispersive shift, which results from the interplay between the time-dependent collective interaction strength and atom-cavity detuning. Controlling the parameters of the atom cloud, we then directly measure the dependence of the dispersive shift on the atom-cavity detuning and on the number of Rydberg atoms. The results are in good agreement with the Tavis-Cummings Hamiltonian in the dispersive regime, and indicate collective coupling strengths of gN/2pi = 1 MHz, which correspond to more than N = 3 · 10^3 Rydberg atoms. This nondestructive detection of Rydberg atoms achieves a relative precision of 4.5% and an accuracy of 20 %, which are both limited by the inhomogeneity of the atom-cavity detuning over the size of the atom cloud. In a second experiment, we reduce the inhomogeneity by decreasing the size of the atomic cloud and employing the triplet Rydberg transition at n = 42, which is less sensitive to dc electric fields. The precision of the atom number detection is further enhanced by increasing the cavity quality factor to Q = 10^5 with a superconducting niobium cavity. The combined improvements result in the nondestructive detection of a few hundred Rydberg atoms with an accuracy of 3% and a precision of 1 %, which is an order of magnitude improvement over the previous experiment. Motivated by these results obtained from averaging over about 4 × 10^4 repetitions of the experiment, we consider the nondestructive detection of the atom number in single-shot measurements with a high number of photons in the cavity. By studying the dispersive shift and the probability to excite the 42p states as functions of the photon number, we find a critical photon number ncrit = 4.4×10^4 close to the estimated value and verify that the excitation probability remains below 2.2% for all photon numbers. For optimal precision, we then use a photon number close to the critical value and perform single-shot measurements of the atom number that show a linear correlation between the results of the nondestructive detection method using the dispersive shift and the destructive detection with a microchannel plate. We achieve a single-shot uncertainty of delta N = 65 in the nondestructive atom number detection, which is close to the width of a Poissonian distribution square-root(N) = 25 for the highest atom numbers N = 600. We estimate that the precision in the single-shot measurements can be further enhanced to delta N = 5 (delta N/N = 1 %) by using quantum-limited amplifiers and increasing the single-shot integration time with Stark deceleration of the Rydberg atoms. Such precise nondestructive single-shot measurements of the number of Rydberg atoms are relevant for the quantitative evaluation of scattering cross-sections in experiments with Rydberg atoms and molecules. Moreover, the demonstrated collective coupling strengths open up the prospect for hybrid cavity QED with Rydberg atoms and superconducting quantum bits in rectangular waveguide cavities.
A numerical analysis of dispersive quantum nondemolition measurement of the photon number of a microwave cavity field is presented. Simulations show that a key property of the dispersive atom-field interaction used in Ramsey interferometry is the extremely high sensitivity of the dynamics of atomic and field states to basic parameters of the system. When a monokinetic atomic beam is sent through a microwave cavity, a qualitative change in the field state can be caused by an uncontrollably small deviation of parameters (such as atom path length through the cavity, atom velocity, cavity mode frequency detuning, or atom-field coupling constants). The resulting cavity field can be either in a Fock state or in a super-Poissonian state (characterized by a large photon-number variance). When the atoms have a random velocity spread, the field is squeezed to a Fock state for arbitrary values of the system’s parameters. However, this makes detection of Ramsey fringes impossible, because the probability of detecting an atom in the upper or lower electronic state becomes a random quantity almost uniformly distributed over the interval between zero and unity, irrespective of the cavity photon number.