A bare bound state is modeled as a ground-state two-level atom which at t=0 is deprived of most of the low-frequency components of its virtual radiation field. This state is expected to evolve into a fully dressed ground state through reconstruction of the full cloud of virtual quanta. The quantum theory of measurement is used to show that the dynamics of the two-level atom due to this reconstruction can be detected experimentally under appropriate conditions. The measuring apparatus is modeled by a pointer coupled to the atom. The theory predicts that for sufficiently short measurements the bound state can be used as a probe of the dressing process. This result is discussed in connection with the theory of the excitonic polaron in a semiconductor.
A bare bound state is modeled as a ground-state two-level atom which at t=0 is deprived of most of the low-frequency components of its virtual radiation field. This state is expected to evolve into a fully dressed ground state through reconstruction of the full cloud of virtual quanta. The quantum theory of measurement is used to show that the dynamics of the two-level atom due to this reconstruction can be detected experimentally under appropriate conditions. The measuring apparatus is modeled by a pointer coupled to the atom. The theory predicts that for sufficiently short measurements the bound state can be used as a probe of the dressing process. This result is discussed in connection with the theory of the excitonic polaron in a semiconductor.
A gedanken experiment is discussed to measure the population of a two-level atom interacting with a single-mode radiation field. The atom-field system is taken to be in the dressed ground state. The measuring apparatus consists of a classical pointer linearly coupled to the atom. It is shown that the result of the measurement depends strongly on the duration τ on the measuring process. For τ shorter than the time of the vacuum fluctuations creating the virtual photon cloud around the atom, the pointer perceives the atom as bare. In the opposite case the atom is perceived by the pointer as dressed or partially dressed. The insight gained in the nature of the virtual photon cloud, in the meaning of the quantum detection process and in the preparation of partially dressed states, is discussed in the light of this result.
Introduction . In this final chapter we review two topics of the literature concerning dressed atoms which are of conceptual relevance and capable of shedding some light on the physical meaning and significance of atomic dressing. The first section is devoted to some recent work in connection with the quantum theory of measurement. We include the measuring apparatus in the Hamiltonian along with an appropriate apparatus-atom coupling. We argue that the theory of measurement of finite duration provides us with a tool for detecting the spectral composition of the virtual cloud surrounding an atom. In fact, we show that in a measurement of duration T on a two-level atom fully dressed by the vacuum fluctuations, as discussed in Chapters 6 and 7, the apparatus perceives the atom as dressed only by photons of frequency larger than T -1 . In the case of a two-level atom dressed by a single-mode field populated by real photons, discussed in Chapter 5, we show that if T is smaller than the inverse Rabi frequency ħΔ -1 , the atom is perceived by the apparatus as bare; on the contrary, if T is larger than ħΔ -1 , the atom is perceived as dressed. The time scales for the two cases of dressing, by vacuum fluctuations or by a real single-mode field, are very different, but the similarity of the effects indicates a common physical aspect of the two kinds of dressing.
We consider a two-level atom in a strong laser field, described by the Jaynes-Cummings Hamiltonian in the rotating-wave approximation, yielding the well known dressed states. Diagonalization of the total Hamiltonian is attained by introducing dressed-atomic and photon operators. The quantum theory of measurement of finite duration is used to explore the nature of the physical observables corresponding to the dressed operators. A measuring apparatus is contrived in order to observe the bare-atomic population and the bare-photon number in a dressed state of the system. It is shown that, if the duration of the measurement is longer than the Rabi period of the system, the apparatus leads to observation of the dressed-atomic population and of the dressed-photon number rather than of the corresponding bare quantities for which it was designed. Conceptual and practical consequences of this result are discussed.
An atom or a molecule is constituted by a set of bound electric charges with dynamics governed by the laws of quantum mechanics. These charges are sources of the quantized electromagnetic field which also binds them together, and thus the effects of their interaction with the field cannot be disregarded in principle. Consequently even overall neutral atoms, on which we focus our attention, are driven by a dynamics which is inextricably related to the dynamics of the quantized electromagnetic field. One of the most prominent aspects of the atom-held interaction is the existence of a cloud of virtual photons which dresses the atom even in the lowest possible energy state of the system. In this paper we review the static as well as the dynamic aspects of the theory of the virtual cloud around the neutral atoms. We begin by reviewing various forms of the atom-field coupling as well as various models of simplified atoms which will be used in the rest of the paper. The question then arises as how to characterize quantitatively the shape of the virtual cloud, and we show that the energy density of the electromagnetic field is a physical quantity suitable for this purpose. First a perturbative approach to calculating this shape is developed and applied to several physical models of a ground-state dressed atom. The next step is to consider virtual clouds which are out of equilibrium and examine their time development. This leads to the concept of half-dressed sources, which are discussed in a different physical context both in the absence and in the presence of real photons. In particular the role of the virtual cloud in ensuring causality of the field propagating in dressing and undressing processes is emphasized. Finally, the nature of the virtual cloud is further discussed in the light of theories concerning the dynamics of an atomic pair, the quantum theory of measurement and the effects of a driving electromagnetic field.
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in general, a very time-consuming task that requires a large number of measurements. There are, however, systems in which the data acquisition can be done more efficiently. In fact, an ensemble of quantum systems can be prepared and manipulated by external fields while being continuously and collectively probed, producing enough information to estimate its state. This provides a basis for continuous measurement quantum tomography. In this protocol, an ensemble of identically prepared systems is collectively probed and controlled in a time-dependent manner to create an informationally complete continuous measurement record. The measurement history is then inverted to determine the state at the initial time. We use two different estimation methods: maximum likelihood and compressed sensing. The general formalism is applied to the case of reconstruction of the quantum state encoded in the magnetic sub-levels of a large-spin alkali atom, 133Cs. We apply this protocol to the case of reconstruction of states in the full 16-dimensional electronic-ground subspace (F=3⊕F=4), controlled by microwaves and radio-frequency magnetic fields. We present an experimental demonstration of continuous measurement quantum tomography in an ensemble of cold cesium atoms with full control of its 16-dimensional Hilbert space. We show the exquisite level of control achieved in the lab and the excellent agreement between the theory discussed in this dissertation and the experimental results. This allows us to achieve fidelities >95% for low complexity quantum states, and >92% for arbitrary random states, which is a formidable accomplishment for a space of this size.
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in general, a very time-consuming task that requires a large number of measurements. There are, however, systems in which the data acquisition can be done more efficiently. In fact, an ensemble of quantum systems can be prepared and manipulated by external fields while being continuously and collectively probed, producing enough information to estimate its state. This provides a basis for continuous measurement quantum tomography. In this protocol, an ensemble of identically prepared systems is collectively probed and controlled in a time-dependent manner to create an informationally complete continuous measurement record. The measurement history is then inverted to determine the state at the initial time. We use two different estimation methods: maximum likelihood and compressed sensing. The general formalism is applied to the case of reconstruction of the quantum state encoded in the magnetic sub-levels of a large-spin alkali atom, 133Cs. We apply this protocol to the case of reconstruction of states in the full 16-dimensional electronic-ground subspace (F=3⊕F=4), controlled by microwaves and radio-frequency magnetic fields. We present an experimental demonstration of continuous measurement quantum tomography in an ensemble of cold cesium atoms with full control of its 16-dimensional Hilbert space. We show the exquisite level of control achieved in the lab and the excellent agreement between the theory discussed in this dissertation and the experimental results. This allows us to achieve fidelities >95% for low complexity quantum states, and >92% for arbitrary random states, which is a formidable accomplishment for a space of this size.