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Physical Review A

Generation of sub-Poissonian photon number distribution

Niels Grønbech‐Jensen, P. S. Ramanujam

Published Mar 1, 1990• 6 citations
Publisher

Abstract

An optimization of a nonlinear Mach-Zehnder interferometer to produce sub-Poissonian photon number distribution is proposed. We treat the system quantum mechanically and estimate the mirror parameters, the nonlinearity of the medium in the interferometer, and the input power to obtain minimal output uncertainty in the photon number. The power efficiency of the system is shown to be high.

DOI
10.1103/physreva.41.2906

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 1, 1991•0 citations
An optimization of a nonlinear Mach-Zehnder interferometer to produce sub-Poissonian photon number distribution is proposed. We treat the system quantum mechanically and estimate the mirror parameters, the nonlinearity of the medium in the interferometer, and the input power to obtain minimal output uncertainty in the photon number. The power efficiency of the system is shown to be high.
The output state of a nonlinear Mach-Zehnder interferometer is shown to be an effective number-phase minimum-uncertainty state with reduced photon-number uncertainty. This interferometer includes an optical Kerr medium in one arm with a coherent-state input. Unusual ``crescent''-shaped squeezing which preserves photon number is revealed in the unitary evolution associated with a self-phase-modulation in the Kerr medium. Photon-number uncertainty 〈\ensuremath{\Delta}n${^}^{2}$〉 can be reduced by interference with a coherent-state reference wave. It can be minimized to 〈n^〉1/3{〉}^{1/3}〉1/3, far below the limit 〈n^〉2/3{〉}^{2/3}〉2/3 achieved by an ordinary squeezed state. The increased phase uncertainty due to self-phase-modulation and the reduced photon-number uncertainty still preserve the minimum-uncertainty product 〈\ensuremath{\Delta}n${^}^{2}$〉〈\ensuremath{\Delta}\ensuremath{\Phi}${^}^{2}$〉\ensuremath{\sim}(1/4). .AE
In this thesis, we study a system consisting of qubits—two-level quantum systems— interacting in the strong-coupling regime for a finite amount of time with a mode of the electromagnetic field inside a resonator. In particular, we are interested in the dynamics of the photon number and the possibility of controlling its statistics to produce sub-Poissonian light. To describe the system we use quantum trajectory theory where the time evolution of the state vector consists of both a continuous part and jumps, which account for the resonator losses. We also incorporate a variable number of qubits (changing in time) interacting with the mode. A computer simulation was developed and optimised to calculate the quantum trajectories. When one sets the qubits initially to the excited state and fixes the interaction time accordingly, so-called “trapping states” (photon numbers which block the addition of a photon by a single qubit) appear. These states are instrumental in the generation of sub-Poisson fields, for some cases even when the number of interacting qubits follow a Poisson process. We take advantage of the existence of trapping states to implement control protocols based on the measurement of the output field of the resonator, with the objective of lowering the uncertainty in the number of photons. Furthermore, we explore the possibility of creating a source of sub-Poissonian pulses by first using a random interaction time (which bypasses the trapping states) and then utilising the control protocols developed. We are able to achieve fields with a Mandel Q parameter of QM = −0.98 and a photon number of n 68.
We study the statistical and phase properties of the output states of a Mach-Zehnder interferometer with a nonlinear Kerr medium in one of its arms. The combination of nonlinearity and displacement produced by the interferometer generates output states (displaced Kerr states) that, unlike those derived from a Kerr medium alone (Kerr states), do not necessarily retain the photon statistics of the initially coherent field. As the parameter characterizing the nonlinear medium is varied, the statistics of the output field vary from sub-Poissonian to super-Poissonian. The photon-number distributions of these states are rationalized by examining their quasiprobability distributions, which vary from banana-shaped for sub-Poissonian statistics to complicated interference structures for highly super-Poissonian statistics. The number-phase properties of the Kerr and displaced Kerr states are studied for the case of small photon numbers (relevant to cavity quantum electrodynamics) using a methodology based on the Pegg-Barnett formalism. In particular, we determine the range of parameters for which the states are minimum-uncertainty states and whether they are squeezed with respect to photon number and phase, drawing a distinction between a sub-Poissonian nature and number squeezing. Finally, we find that sub-Poissonian statistics can coexist with quadrature squeezing for a range of parameters.
Using an extension of the Scully—Lamb laser theory we show that by insertion of nonlinear elements in the cavity, laser light with nonclassical sub—Poissonian photon statistics can be generated. For an N—photon absorber in the limit of small saturation the variance of the photon number distribution can be reduced by a factor of (+1/N) compared to Poissonian limit of the usual laser. When we generalize the type of such nonlinear elements to the case of a nonlinear feedback or Raman type nonlinear transition, the noise in the laser intensity can be reduced even further and approach the ideal limit, characterized by a Mandel Q parameter of Q = —1. Furthermore we show how this noise reduction via nonlinearities can be combined with a regular pump mechanism, which recently has been sugessted as a way to generate sub—Poissonian light. It turns out that in certain configurations the effect of both methods can be combined. Finally we show how this nonclassical behaviour is also reflected in a reduction of the output intensity power spectra below the shot noise level.