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Physical Review A

Tunneling in the presence of driving in a cavity that contains a Kerr medium and is parametrically pumped

B. F. Wielinga, Gerard J Milburn

Published Jun 1, 1994• 8 citations
Publisher

Abstract

Driving is applied to an optical system consisting of a Kerr medium combined with a second-order parametric process driven by a pump field which is sinusoidally modulated in amplitude. The coherent tunneling in this system is found to be both enhanced and suppressed by this, depending on the frequency of the driving chosen. A variation of time-independent perturbation theory is applied to this system and found to successfully describe this behavior.

DOI
10.1103/physreva.49.5042

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Driving is applied to an optical system consisting of a Kerr medium combined with a second-order parametric process driven by a pump field which is sinusoidally modulated in amplitude. The coherent tunneling in this system is found to be both enhanced and suppressed by this, depending on the frequency of the driving chosen. A variation of time-independent perturbation theory is applied to this system and found to successfully describe this behavior.
The second-order perturbation theory in the framework of the Kramers-Henneberger oscillating frame representation of the Hamiltonian [H. A. Kramers, Quantum Mechanics (North-Holland, Amsterdam, 1956); W. C. Henneberger, Phys. Rev. Lett. 21, 838 (1968)] is used to study the tunneling process in a periodically driven double-well potential. The eigenstates of the Floquet Hamiltonian are efficiently approximated when a field frequency is larger than a classical frequency of the time-averaged Hamiltonian. The conditions for coherent enhancement and suppression of tunneling are obtained when the standard perturbation theory fails. It is shown that the enhancement and suppression of tunneling is due to field-induced coupling between states of a one-period averaged effective potential.
This work investigates photon blockade control in a hybrid quantum system containing a Kerr-nonlinear cavity coupled to an optical parametric amplifier (OPA). The dynamics are governed by a master equation derived from an effective Hamiltonian that includes cavity decay. To obtain analytical solutions, the system's quantum state is expanded in the Fock basis up to the two-photon level. Solving the steady-state Schrodinger equation yields probability amplitudes and the analytical conditions for optimal photon blockade. Results confirm that photon blockade is achievable with suitable parameters. Excellent agreement is found between the analytical solutions and numerical simulations for the steady-state, equal-time second-order correlation function, validating both the analytical method and the blockade effect. Numerically, the average intracavity photon number increases significantly under resonance, providing a theoretical pathway for enhancing single-photon source brightness. Furthermore, the driving phase is shown to regulate the optimal blockade region: it shifts the parabolic region within the two-dimensional parameter space of driving strength and OPA nonlinearity and can even reverse its opening direction. The influence of Kerr nonlinearity is also examined. Photon blockade remains robust across a wide range of Kerr strengths. Physical analysis attributes the effect to destructive quantum interference between two distinct excitation pathways that suppress two-photon states. While Kerr nonlinearity shifts the system's energy levels, it does not disrupt this interference mechanism, explaining the effect's stability over a broad parameter range.
The response of a system of coherently pumped atoms to weak electromagnetic perturbing fields is discussed in general terms. The pump field is prescribed, and is assumed to propagate unattenuated through the medium which the (identical) atoms comprise, exciting a particular transition through either electric or magnetic dipole coupling. The perturbing field, which is assumed to act through electric dipole coupling, is allowed to be the (resonant) field emitted by the atoms, a weak external field absorbed by the atoms under resonant conditions, or a resonant or nonresonant wave propagating through the pumped medium. All of these cases are conveniently described within the same general framework, based on an analysis of the (single-atom) two-time dipole-moment correlation function. This function contains nonstationary components as well as stationary ones, owing to the time dependence imposed by the pump field. We are accordingly led to introduce a time-dependent linear susceptibility, which is inhomogeneous and anisotropic, due, respectively, to the variation of the pump phase within the medium and the preferred direction established by the pump-field polarization. Such disparate effects as parametric frequency conversion, emission- and absorption-line splitting, and time-dependent modulation of resonant emission and absorption functions in optical-pumping experiments emerge naturally from a single unified formalism.