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Physical Review A

Linear optical extraction of photon-number Fock states from coherent states

Kaoru Sanaka

Published Feb 4, 2005• 29 citations
Publisher

Abstract

Photon-number Fock states play important roles in quantum optics. However, the generation of the states are very difficult because of the lack of large effective nonlinearities. In this Rapid Communication, I show a scheme to produce the Fock state from an input coherent state by using only linear optics method and projection measurements. I analyze the case of five-photon number state generation from coherent states for a specific case of the scheme. It is possible to remove the vacuum state from the output state when one introduces quantum nondemolition measurement that can also be implemented with all linear optics setup.

DOI
10.1103/physreva.71.021801

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Photon-number Fock states play important roles in quantum optics. However, the generation of the states are very difficult because of the lack of large effective nonlinearities. In this Rapid Communication, I show a scheme to produce the Fock state from an input coherent state by using only linear optics method and projection measurements. I analyze the case of five-photon number state generation from coherent states for a specific case of the scheme. It is possible to remove the vacuum state from the output state when one introduces quantum nondemolition measurement that can also be implemented with all linear optics setup.
We use a photon-number-resolving detector to monitor the photon-number distribution of the output of an interferometer, as a function of phase delay. As inputs we use coherent states with mean photon number up to seven. The postselection of a specific Fock (photon-number) state effectively induces high-order optical nonlinearities. Following a scheme by Bentley and Boyd [Opt. Express 12, 5735 (2004).10.1364/OPEX.12.005735], we explore this effect to demonstrate interference patterns a factor of 5 smaller than the Rayleigh limit.
We analyze the linear optical realization of number-sum Bell measurement and number-state manipulation by taking into account the realistic experimental situation, specifically imperfectness of single-photon detector. The present scheme for number-state manipulation is based on the number-sum Bell measurement, which is implemented with linear optical elements, i.e., beam splitters, phase shifters, and zero-one-photon detectors. Squeezed vacuum states and coherent states are used as optical sources. The linear optical Bell state detector is formulated quantum theoretically with a probability operator measure. Then, the fidelity of manipulation and preparation of number states, particularly for qubits and qutrits, is evaluated in terms of the quantum efficiency and dark count of single-photon detector. It is found that a high fidelity is achievable with small enough squeezing parameters and coherent state amplitudes.
The authors begin by summarizing some schemes of generating finite-dimensional (FD) quantum-optical states. Although it is possible to generate n-photon Fock states and then to construct a desired state from these states, the focus of the chapter is on generation schemes that lead directly to the FD coherent states and FD squeezed vacuum. The method described is based on the quantum nonlinear oscillator evolution. The oscillator is assumed to be driven by external excitation. Depending on the character of the excitation, various FD states can be produced.
Multi-mode NOON states have been attracting increasing attentions recently for their abilities of obtaining supersensitive and superresolved measurements for simultaneous multiple-phase estimation. In this paper, four different methods of generating multi-mode NOON states with a high photon number were proposed. The first method is a linear optical approach that makes use of the Fock state filtration to reduce lower-order Fock state terms from the coherent state inputs, which are jointly combined to produce a multi-mode NOON state with the triggering of multi-fold single-photon coincidence detections (SPCD) and appropriate postselection. The other three methods (two linear and one nonlinear) use N-photon Fock states as the inputs and require SPCD triggering only. All of the four methods can theoretically create a multi-mode NOON state with an arbitrary photon number. Comparisons among these four methods were made with respect to their feasibility and efficiency. The first method is experimentally most feasible since it takes considerably fewer photonic operations and, more importantly, requires neither the use of high-N Fock states nor high-degree of nonlinearity.
We report preparation and characterization of coherent superposition states t[0>+alpha]1> of the electromagnetic field by conditional measurements on a beam splitter. This state is generated in one of the beam splitter output channels if a coherent state [alpha> and a single-photon Fock state [1> are present in the two input ports and a single photon is registered in the other beam splitter output. The single photon thus plays a role of a "catalyst:" it is explicitly present in both the input and the output channels of the interaction yet facilitates generation of a nonclassical state of light.