The quantum mechanics we use in quantum optics is rather different from that taught in the standa... more The quantum mechanics we use in quantum optics is rather different from that taught in the standard quantum mechanics course. It is, of course, the same quantum mechanics; but the emphasis is different. Two observations illustrate what I mean. First, quantum optics emphasizes dissipative systems, open systems. The most notable of these is the laser, but a rather long list could be given which would include close relatives such as the parametric oscillator and a litany of systems involving resonance fluorescence. Second, quantum optics has always had close ties to the issue of quantum measurement. This theme goes back to the beginnings of the subject and Glauber’s quantum theory of coherence, which is founded on the multi-coincidence rates measured in photoelectric detection.
Reference is made to the observation by several investigators that in a high-finesse cavity, Iked... more Reference is made to the observation by several investigators that in a high-finesse cavity, Ikeda's (1979, 1980) instability most readily occurs with the injected field tuned midway between cavity resonances. It is noted that the fundamental period of oscillation, at twice the cavity round-trip time, is just the beat frequency between the injected field and the adjacent cavity modes. It is shown here that a very general symmetry underlies this observation. This symmetry identifies an entire class of multimode instabilities in a cavity tuned between resonances as counterparts to conventional optical bistability. Given a short medium-response time or a long cavity, where cavity dynamics are described by a nonlinear map, a one-to-one correspondence exists between bistable and oscillatory systems. In this case, the theory of both absorptive and dispersive bistability can be transferred wholesale to a description of corresponding oscillatory instabilities. What is more, the ensuring oscillations occur between states on the S-shaped bistability curves. A simple relationship converts the theory of optical bistability into a theory of multimode instability and self-oscillation in a ring cavity excited between cavity resonances.
The driven Jaynes-Cummings model shows collapses and revivals of the mean photon number on a time... more The driven Jaynes-Cummings model shows collapses and revivals of the mean photon number on a time scale much longer than the revival time for the two-state inversion. The behavior is essentially that of a nonlinear quantum oscillator with Hamiltonian {ital H}={radical}({cflx {ital A}}{sup {degree}}+{alpha})({cflx {ital A}}+{alpha}). {copyright} {ital 1996 The American Physical Society.}
We solve the spontaneous-emission problem for an atom coupled to a standing-wave cavity mode. The... more We solve the spontaneous-emission problem for an atom coupled to a standing-wave cavity mode. The interaction between the atom and the cavity mode is treated nonperturbatively with the quantized motion of the atom along the cavity axis included. Results are presented for the spontaneous-emission spectrum and the final momentum distribution of the atom. For equal atomic and cavity linewidths analytical
Recent studies of the decoherence induced by the quantum nature of the laser field driving a two-... more Recent studies of the decoherence induced by the quantum nature of the laser field driving a two-state atom [J. Gea-Banacloche, Phys. Rev. A 65, 022308 (2002); S. J. van Enk and H. J. Kimble, Quantum Inf. Comput. 2, 1 (2002)] have been questioned by Itano [W. M. Itano, Phys. Rev. A 68, 046301 (2003)] and the proposal made that all decoherence is due to spontaneous emission. We analyze the problem within the formalism of cascaded open quantum systems. Our conclusions agree with the Itano proposal. We show that the decoherence, nevertheless, may be divided into two parts---that due to forwards scattering and to scattering out of the laser mode. Previous authors attribute the former to the quantum nature of the laser field.
Conditional homodyne detection is proposed as an extension of the intensity correlation technique... more Conditional homodyne detection is proposed as an extension of the intensity correlation technique introduced by Hanbury-Brown and Twiss [Nature (London) 177, 27 (1956)]. It detects giant quadrature amplitude fluctuations for weakly squeezed light, violating a classical bound by orders of ...
Under conditions of strong dipole coupling an optical cavity containing one atom behaves as a two... more Under conditions of strong dipole coupling an optical cavity containing one atom behaves as a two-state system when excited near one of the ``vacuum'' Rabi resonances. A coherent driving field induces a dynamic Stark splitting of the ``vacuum'' Rabi resonance. We demonstrate this two-state behavior in computer experiments based on quantum trajectory simulations.
The quantum mechanics we use in quantum optics is rather different from that taught in the standa... more The quantum mechanics we use in quantum optics is rather different from that taught in the standard quantum mechanics course. It is, of course, the same quantum mechanics; but the emphasis is different. Two observations illustrate what I mean. First, quantum optics emphasizes dissipative systems, open systems. The most notable of these is the laser, but a rather long list could be given which would include close relatives such as the parametric oscillator and a litany of systems involving resonance fluorescence. Second, quantum optics has always had close ties to the issue of quantum measurement. This theme goes back to the beginnings of the subject and Glauber’s quantum theory of coherence, which is founded on the multi-coincidence rates measured in photoelectric detection.
Reference is made to the observation by several investigators that in a high-finesse cavity, Iked... more Reference is made to the observation by several investigators that in a high-finesse cavity, Ikeda's (1979, 1980) instability most readily occurs with the injected field tuned midway between cavity resonances. It is noted that the fundamental period of oscillation, at twice the cavity round-trip time, is just the beat frequency between the injected field and the adjacent cavity modes. It is shown here that a very general symmetry underlies this observation. This symmetry identifies an entire class of multimode instabilities in a cavity tuned between resonances as counterparts to conventional optical bistability. Given a short medium-response time or a long cavity, where cavity dynamics are described by a nonlinear map, a one-to-one correspondence exists between bistable and oscillatory systems. In this case, the theory of both absorptive and dispersive bistability can be transferred wholesale to a description of corresponding oscillatory instabilities. What is more, the ensuring oscillations occur between states on the S-shaped bistability curves. A simple relationship converts the theory of optical bistability into a theory of multimode instability and self-oscillation in a ring cavity excited between cavity resonances.
The driven Jaynes-Cummings model shows collapses and revivals of the mean photon number on a time... more The driven Jaynes-Cummings model shows collapses and revivals of the mean photon number on a time scale much longer than the revival time for the two-state inversion. The behavior is essentially that of a nonlinear quantum oscillator with Hamiltonian {ital H}={radical}({cflx {ital A}}{sup {degree}}+{alpha})({cflx {ital A}}+{alpha}). {copyright} {ital 1996 The American Physical Society.}
We solve the spontaneous-emission problem for an atom coupled to a standing-wave cavity mode. The... more We solve the spontaneous-emission problem for an atom coupled to a standing-wave cavity mode. The interaction between the atom and the cavity mode is treated nonperturbatively with the quantized motion of the atom along the cavity axis included. Results are presented for the spontaneous-emission spectrum and the final momentum distribution of the atom. For equal atomic and cavity linewidths analytical
Recent studies of the decoherence induced by the quantum nature of the laser field driving a two-... more Recent studies of the decoherence induced by the quantum nature of the laser field driving a two-state atom [J. Gea-Banacloche, Phys. Rev. A 65, 022308 (2002); S. J. van Enk and H. J. Kimble, Quantum Inf. Comput. 2, 1 (2002)] have been questioned by Itano [W. M. Itano, Phys. Rev. A 68, 046301 (2003)] and the proposal made that all decoherence is due to spontaneous emission. We analyze the problem within the formalism of cascaded open quantum systems. Our conclusions agree with the Itano proposal. We show that the decoherence, nevertheless, may be divided into two parts---that due to forwards scattering and to scattering out of the laser mode. Previous authors attribute the former to the quantum nature of the laser field.
Conditional homodyne detection is proposed as an extension of the intensity correlation technique... more Conditional homodyne detection is proposed as an extension of the intensity correlation technique introduced by Hanbury-Brown and Twiss [Nature (London) 177, 27 (1956)]. It detects giant quadrature amplitude fluctuations for weakly squeezed light, violating a classical bound by orders of ...
Under conditions of strong dipole coupling an optical cavity containing one atom behaves as a two... more Under conditions of strong dipole coupling an optical cavity containing one atom behaves as a two-state system when excited near one of the ``vacuum'' Rabi resonances. A coherent driving field induces a dynamic Stark splitting of the ``vacuum'' Rabi resonance. We demonstrate this two-state behavior in computer experiments based on quantum trajectory simulations.
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Papers by H. Carmichael