The properties of an electron in an atom or molecule are not fixed; rather they are a function of the optical environment of the emitter. Not only is the spontaneous emission a function of the optical environment, but also the underlying wave functions and energy levels, which are modified by the potential induced by quantum fluctuations of the electromagnetic field. In free space, this modification of atomic levels and wave functions is very weak and generally hard to observe due to the prevalence of other perturbations like fine structure. Here, we explore the possibility of highly tailorable electronic structure by exploiting large Lamb shifts in tunable electromagnetic environments such as graphene, whose optical properties are dynamically controlled via doping. The Fermi energy can be chosen so that the Lamb shift is very weak, but it can also be chosen so that the shifts become more prominent than the fine structure of the atom and even potentially the Coulomb interaction with the nucleus. Potential implications of this idea include being able to electronically shift an unfavorable emitter structure into a favorable one, a new approach to probe near-field physics in fluorescence, and a way to access regimes of physics where vacuum fluctuations are not a weak perturbation but rather the dominant physics.
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 natural atom placed into a cavity with time-dependent parameters can be parametrically excited due to interaction with the quantized photon mode. One of the channels for this process is the dynamical Lamb effect, induced by a nonadiabatic modulation of the atomic-level Lamb shift. However, in experiments with natural atoms it is quite difficult to isolate this effect from other mechanisms of atom excitation. We point out that a transmission line cavity coupled with a superconducting qubit (an artificial macroscopic atom) provides a unique platform for observation of the dynamical Lamb effect. A key idea is to exploit a dynamically tunable qubit-resonator coupling, which was implemented quite recently. By varying the coupling nonadiabatically, it is possible to parametrically excite a qubit through a nonadiabatic modulation of the Lamb shift, even if the cavity was initially empty. The dynamics of such a coupled system is studied within the Rabi model with a time-dependent coupling constant and beyond the rotating-wave approximation. An efficient method to increase the effect through the periodic and nonadiabatic switching of the qubit-resonator coupling energy is proposed.
\abstract{The Lamb shift, one of the most fundamental interactions in atomic physics, arises from the interaction of H atoms with the electromagnetic fluctuations of the quantum vacuum. The energy shift has been computed in a variety of ways. The energy shift, as Feynman and Power demonstrated, equals the change in the vacuum energy in the volume containing the H atoms due to the change in the index of refraction arising from the presence of the H atoms. By using this result and a group theoretical calculation of the contribution to the Lamb shift from each frequency of the vacuum fluctuations, we can obtain an expression for the size of the region of vacuum energy for each frequency \texorpdfstring{
ω}{ω} around the H atom due to the Lamb shift. The ground state atom is surrounded by a region of positive vacuum energy that extends well beyond the atom for low frequencies. This region can be described as a steady state cloud of virtual quanta. For energies \texorpdfstring{
E=ℏω}{E=hbar omega} eV less than 1 eV, the radius of the positive energy region is approximately 14. 4/E Angstroms. For a vacuum fluctuation of wavelength \texorpdfstring{
λ}{lambda} the radius is \texorpdfstring{
(α/2π)λ}{(alpha/2pi) lambda}. Thus, for long wavelengths, the region has macroscopic dimensions. The energy-time Uncertainty Relation predicts a maximum possible radius that is larger than this by a factor of \texorpdfstring{
1/4α}{1/(4 alpha)}.}
\keyword{Bethe; radiative shift; shift spectral density; spectral volume; vacuum fluctuations; vacuum field; Lamb shift; QED; energy field, renormalization, zero point fluctuations; hydrogen atom}.