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Physical Review Letters

Filtering Out Photonic Fock States

Kaoru Sanaka, Kevin J. Resch, Anton Zeilinger

Published Feb 27, 2006• 85 citations
Publisher

Abstract

Unprecedented optical nonlinearities can be generated probabilistically in simple linear-optical networks conditioned on specific measurement outcomes. We describe a highly controllable quantum filter for photon number states, which takes advantage of such a measurement-induced amplitude nonlinearity. The basis for this filter is multiphoton nonclassical interference which we demonstrate for one- and two-photon states over a wide range of beam splitter reflectivities. Specifically, we show that the transmission probability, conditional on a specific measurement outcome, can be larger for a two-photon state than a one-photon state; this is not possible with linear optics alone.

DOI
10.1103/physrevlett.96.083601

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Unprecedented optical nonlinearities can be generated probabilistically in simple linear-optical networks conditioned on specific measurement outcomes. We describe a highly controllable quantum filter for photon number states, which takes advantage of such a measurement-induced amplitude nonlinearity. The basis for this filter is multiphoton nonclassical interference which we demonstrate for one- and two-photon states over a wide range of beam splitter reflectivities. Specifically, we show that the transmission probability, conditional on a specific measurement outcome, can be larger for a two-photon state than a one-photon state; this is not possible with linear optics alone.
We develop a technique for generating multiphoton nonclassical states via interference between coherent and Fock states using quantum catalysis. By modulating the coherent field strength, the number of catalyst photons, and the ratio of the beam splitter upon which they interfere, a wide range of nonclassical phenomena can be created, including squeezing of up to 1.25 dB, antibunched and superbunched photon statistics, and states exhibiting over 90% fidelity to displaced coherent superposition states. We perform quantum catalysis experimentally, showing tunability into the nonclassical regime. Our protocol is not limited by weak nonlinearities that underlie most known strategies of preparing multiphoton nonclassical states. Successive iterations of this protocol can lead to direct control over the weights of higher-order terms in the Fock basis, paving the way towards conditional preparation of ``designer'' multiphoton states for applications in quantum computation, communication, and metrology.
We discuss a device capable of filtering out two-mode states of light with mode populations differing by more than a certain threshold, while not revealing which mode is more populated. It would allow engineering of quantum states of light in a way which is preserving specific superpositions. As a result, it would enhance optical phase estimation with these states as well as distinguishability of macroscopic qubits. We propose an optical scheme, which is a relatively simple, albeit non-ideal, operational implementation of such a filter. It uses tapping of the original polarization two-mode field, with a polarization neutral beam splitter of low reflectivity. Next, the reflected beams are suitably interfered on a polarizing beam splitter. It is oriented such that it selects unbiased polarization modes with respect to the original ones. The more an incoming two-mode Fock state is unequally populated, the more the polarizing beam splitter output modes are equally populated. This effect is especially pronounced for highly populated states. Additionally, for such states we expect strong population correlations between the original fields and the tapped one. Thus, after a photon-number measurement of the polarizing beam splitter outputs, a feed-forward loop can be used to let through a shutter the field, which was transmitted by the tapping beam splitter. This happens only if the counts at the outputs are roughly equal. In such a case, the transmitted field differs strongly in occupation number of the two modes, while information on which mode is more populated is non-existent (a necessary condition for preserving superpositions).
We discuss a device capable of filtering out two-mode states of light with mode populations differing by more than a certain threshold, while not revealing which mode is more populated. It would allow engineering of macroscopic quantum states of light in a way which is preserving specific superpositions. As a result, it would enhance optical phase estimation with these states as well as distinguishability of ``macroscopic'' qubits. We propose an optical scheme, which is a relatively simple, albeit nonideal, operational implementation of such a filter. It uses tapping of the original polarization two-mode field, with a polarization-neutral beam splitter of low reflectivity. Next, the reflected beams are suitably interfered on a polarizing beam splitter. It is oriented such that it selects unbiased polarization modes with respect to the original ones. The more an incoming two-mode Fock state is unequally populated, the more the polarizing beam-splitter output modes are equally populated. This effect is especially pronounced for highly populated states. Additionally, for such states we expect strong population correlations between the original fields and the tapped one. Thus, after a photon-number measurement of the polarizing beam-splitter outputs, a feed-forward loop can be used to let through a shutter the field, which was transmitted by the tapping beam splitter. This happens only if the counts at the outputs are roughly equal. In such a case, the transmitted field differs strongly in occupation number of the two modes, while information on which mode is more populated is nonexistent (a necessary condition for preserving superpositions).
In this Letter, we present a simple and versatile scheme for enhancing the nonclassical properties of light states using only linear optics and photodetectors. By combining a coherent state |α〉 and an arbitrary pure state of light |ϕ〉 (excluding coherent states) at two beam splitters, we show that the amplitude α of the coherent state can be tuned to filter out specific Fock components and generate states of light with increased nonclassical features. We provide two examples of input states and demonstrate the effectiveness of our scheme in enhancing the sub-Poissonian statistics or the quadrature squeezing of the output states.
We study multiphoton quantum-interference effects at a beam splitter and its connection to the prospect of attaining interferometric phase-shift measurements with noise levels below the standard quantum limit. Specifically, we consider the mixing of the most classical states of light coherent states with the most nonclassical states of light number states at a 50 : 50 beam splitter. Multiphoton quantum-interference effects from mixing photon-number states of small photon numbers with coherent states of arbitrary amplitudes are dramatic even at the level of a single photon. For input vacuum and coherent states, the joint photon-number distribution after the beam splitter is unimodal, a product of Poisson distributions for each of the output modes but with the input of a single photon, the original distribution is symmetrically bifurcated into a bimodal distribution. With a two-photon-number state mixed with a coherent state, a trimodal distribution is obtained, etc. The obtained distributions are shown to be structured so as to be conducive for approaching Heisenberg-limited sensitivities in photon-number parity-based interferometry. We show that mixing a coherent state with even a single photon results in a significant reduction in noise over that of the shot-noise limit. Finally, based on the results of mixing coherent light with single photons, we consider the mixing coherent light with the squeezed vacuum and the squeezed one-photon states and find the latter yields higher sensitivity in phase-shift measurements for the same squeeze parameter owing to the absence of the vacuum state.
We demonstrate a Fock-state filter which is capable of preferentially blocking single photons over photon pairs. The large conditional nonlinearities are based on higher-order quantum interference, using linear optics, an ancilla photon, and measurement. We demonstrate that the filter acts coherently by using it to convert unentangled photon pairs to a path-entangled state. We quantify the degree of entanglement by transforming the path information to polarization information; applying quantum state tomography we measure a tangle of T=(20+/-9)%.