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arXiv:1012.1014 · Open Systems & Information Dynamics

Vacuum Rabi Oscillation in Nonzero Temperature Open Cavity

Patrycja Stefańska, Marcin Wilczewski, Marek Czachor

Published Dec 1, 2011• 0 citations
arXivHTMLPDF

Abstract

Comparison of the theory of Rabi oscillations with experiment [M. Wilczewski and M. Czachor, Phys. Rev. A 79, 033836 (2009)] suggests that cavity lifetime parameters obtained in measurements with many photons may be much smaller than those applicable to almost vacuum states of light. In this context, we show that the conclusion remains unchanged even if one takes a more realistic description of the initial state of light in cavity.

DOI
10.1142/s123016121100025x

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Comparison of the theory of Rabi oscillations with experiment [M. Wilczewski and M. Czachor, Phys. Rev. A 79, 033836 (2009)] suggests that cavity lifetime parameters obtained in measurements with many photons may be much smaller than those applicable to almost vacuum states of light. In this context, we show that the conclusion remains unchanged even if one takes a more realistic description of the initial state of light in cavity.
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The 1996 experiment by Brune et al. [Phys. Rev. Lett. 76, 1800 (1996)] on vacuum Rabi oscillation is analyzed by means of alternative models of atom-reservoir interaction. Agreement with experimental Rabi oscillation data can be obtained if one defines jump operators in the dressed-state basis and takes into account thermal fluctuations between dressed states belonging to the same manifold. Such low-frequency transitions could be ignored in a closed cavity, but the cavity employed in the experiment was open, which justifies our assumption. The cavity quality factor corresponding to the data is approximately $Q=3.31\ifmmode\times\else\texttimes\fi{}{10}^{10}$, whereas QQQ reported in the experiment was $Q=7\ifmmode\times\else\texttimes\fi{}{10}^{7}$. The rate of decoherence arising from opening of the cavity can be of the same order as an analogous correction coming from finite time resolution $\ensuremath{\Delta}t$ (formally equivalent to collisional decoherence). Peres-Horodecki separability criterion shows that the rate at which the atom-field state approaches a separable state is controlled by fluctuations between dressed states from the same manifold and not by the rate of transitions toward the ground state. In consequence, improving the QQQ factor we do not improve the coherence properties of the cavity.
When an atom is strongly coupled to a cavity, the two systems can exchange a single photon through a coherent Rabi oscillation. This process enables precise quantum-state engineering and manipulation of atoms and photons in a cavity, which play a central role in quantum information and measurement. Recently, a new regime of cavity QED was reached experimentally where the strength of the interaction between light and artificial atoms (qubits) becomes comparable to the atomic transition frequency or the resonance frequency of the cavity mode. Here we show that this regime can strongly modify the concept of vacuum Rabi oscillations, enabling multiphoton exchanges between the qubit and the resonator. We find that experimental state-of-the-art circuit-QED systems can undergo two- and three-photon vacuum Rabi oscillations. These anomalous Rabi oscillations can be exploited for the realization of efficient Fock-state sources of light and complex entangled states of qubits.
Cavity qed is the domain of quantum optics which studies the behaviour of single atoms and photons coupled together in an electromagnetic resonator. During the last ten years, various spectacular effects have been observed on such systems, either on the atom’s or on the field’s properties. The presence of a cavity around an atom can produce an alteration of the atomic radiative rates which has been observed in several experiments. Ideally, cavity qed deals with two-level atoms coupled resonantly or nearly resonantly to a single cavity mode. This is of course a simplification of real situations, in which atoms have many levels and the cavity sustains more than one mode. The amplitudes associated to the upper and lower atomic states oscillate as a function of time, revealing the ‘vacuum Rabi oscillation’ effect. The amplitudes associated to the upper and lower atomic states oscillate as a function of time, revealing the ‘vacuum Rabi oscillation’ effect.
The quantum electrodynamics of an atom in a cavity is reexamined from the view point of the vacuum-field Rabi oscillations. Many features of such oscillations in a single atom as well as in a cooperative system are discussed. Various physical quantities that carry the signature of these vacuum-field oscillations are calculated. Even oscillator systems are shown to exhibit such vacuum-field Rabi oscillations, which is in contrast to the external-field-induced Rabi oscillations. Such oscillations are found to occur in situations involving both single-photon and multiphoton transitions.
The quantum properties of electromagnetic, mechanical or other harmonic oscillators can be revealed by investigating their strong coherent coupling to a single quantum two level system in an approach known as cavity quantum electrodynamics (QED). At temperatures much lower than the characteristic energy level spacing the observation of vacuum Rabi oscillations or mode splittings with one or a few quanta asserts the quantum nature of the oscillator. Here, we study how the classical response of a cavity QED system emerges from the quantum one when its thermal occupation-or effective temperature-is raised gradually over 5 orders of magnitude. In this way we explore in detail the continuous quantum-to-classical crossover and demonstrate how to extract effective cavity field temperatures from both spectroscopic and time-resolved vacuum Rabi measurements.