Quantum Electrodynamics of a Qubit

Abstract

A detailed understanding of the basic physical laws governing the exchange of quantum information, as well as the interaction between material qubits and the quantized electromagnetic field, is of central importance for realizing quantum information networks and for suppressing decoherence due to spontaneous emission of photons. In this section, some basic physical aspects of this interaction are explored in the special case of a single material qubit. The energy exchange between a material qubit interacting with the electromagnetic field is dominated by the absorption and emission of photons [1]. Whereas absorption and stimulated emission of photons is conditioned on photons which are already present in the electromagnetic field, spontaneous emission of photons occurs randomly and even if the electromagnetic field is in its ground state (vacuum) [2]. It is this random and uncontrollable feature of this latter process which causes spontaneous decay and decoherence of qubits. Therefore, suppressing its undesired and uncontrollable features is one of the major challenges in the context of quantum information processing. For this purpose powerful error correction methods have been designed recently [3–5]. Alternatively, spontaneous decay of qubits can also be suppressed at least partially by an appropriate engineering of their coupling to the electromagnetic field. The quantum dynamics of a material qubit interacting with the electromagnetic field depend significantly on the structure of the field modes. If a qubit is coupled to a single-field mode only, its quantum state can be transferred to the field mode and back again in a reversible way as described by the Jaynes–Cummings–Paul model [6,7]. This reversible energy exchange manifests itself in vacuum Rabi oscillations of the qubit between its excited state and its ground state, for example [7]. But with increasing number of interacting field modes this reversible character of the qubit–field dynamics is lost gradually [8–11]. In particular, in the limit of a continuum of accessible field modes the reversibility of the state exchange between qubit and field is lost completely. Typically, under such circumstances an initially excited qubit decays to its ground state spontaneously [12]. As a result, a controllable and reversible transfer of the quantum state of such a qubit to the electromagnetic field and back again becomes impossible. In general, the spontaneous decay rate of the qubit depends on the density of field modes it is coupled to. For purposes of processing quantum information, for example, this latter dependence can be exploited for suppressing spontaneous decay process by an appropriate engineering of the mode structure of the electromagnetic field [13]. Photonic crystals [14] are particularly well suited for this purpose. In this section, we discuss basic physical aspects of the interaction between a single qubit and the electromagnetic field. In particular, we focus on the following main questions: How