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Physical Review Letters

Quantum State Preparation and Conditional Coherence

Kevin J. Resch, Jeff S. Lundeen, Aephraim M. Steinberg

Published Mar 1, 2002• 103 citations
Publisher

Abstract

It is well known that spontaneous parametric down-conversion can be used to probabilistically prepare single-photon states. We have performed an experiment in which arbitrary superpositions of zero- and one-photon states can be prepared by appropriate postselection. The optical phase, which is meaningful only for superpositions of photon number, is related to the relative phase between the zero- and one-photon states. Whereas the light from spontaneous parametric down-conversion has an undefined phase, we show that this technique collapses one beam to a state of well-defined optical phase when a measurement succeeds on the other beam.

DOI
10.1103/physrevlett.88.113601

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It is well known that spontaneous parametric down-conversion can be used to probabilistically prepare single-photon states. We have performed an experiment in which arbitrary superpositions of zero- and one-photon states can be prepared by appropriate postselection. The optical phase, which is meaningful only for superpositions of photon number, is related to the relative phase between the zero- and one-photon states. Whereas the light from spontaneous parametric down-conversion has an undefined phase, we show that this technique collapses one beam to a state of well-defined optical phase when a measurement succeeds on the other beam.
Over a century after the modern prediction of the existence of individual particles of light by Albert Einstein, a reliable source of this simple quantum state of one photon does not exist. While common light sources such as a light bulb, LED, or laser can produce a pulse of light with an average of one photon, there is (currently) no way of knowing the number of photons in that pulse without first absorbing (and thereby destroying) them. Spontaneous parametric down-conversion, a process in which one high-energy photon splits into two lower-energy photons, allows us to prepare a single-photon state by detecting one of the photons, which then heralds the existence of its twin. This process has been the workhorse of quantum optics, allowing demonstrations of a myriad of quantum processes and protocols, such as entanglement, cryptography, superdense coding, teleportation, and simple quantum computing demonstrations. All of these processes would benefit from better engineering of the underlying down-conversion process, but despite significant effort (both theoretical and experimental), optimization of this process is ongoing. The focus of this work is to optimize certain aspects of a down-conversion source, and then use this tool in novel experiments not otherwise feasible. Specifically, the goal is to optimize the heralding efficiency of the down-conversion photons, i.e., the probability that if one photon is detected, the other photon is also detected. This source is then applied to two experiments (a single-photon source, and a quantum cryptography implementation), and the detailed theory of an additional application (a source of Fock states and path-entangled states, called N00N states) is discussed, along with some other possible applications.
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.
We demonstrate experimentally a phase measurement using general two-photon superposition states in a multiport interferometer shown schematically. A pair of photons, produced in the process of spontaneous parametric down-conversion, is transformed into the desired superposition state using beam splitters BS1 and BS2, provided that no photon escapes through the unmonitored port of BS2. In the signal arm, the photon pair experiences losses introduced by the beam splitter BS3 and monitored by a detector C, and subsequently probes the phase shift phi. The phase information is read out by sending the photons onto the beam splitter BS4, whose output ports are monitored by detectors A and B.