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The Journal of Chemical Physics

Quantum optical measurement with tripartite entangled photons generated by triple parametric down-conversion

Minhaeng Cho

Published May 11, 2018• 2 citations
Publisher

Abstract

Parametric down-conversion is a second-order nonlinear optical process annihilating a pump photon and creating a pair of photons in the signal and idler modes. Then, by using two parametric down-converters and introducing a path indistinguishability for the two generated idler modes, a quantum coherence between two conjugate signal beams can be induced. Such a double spontaneous or stimulated parametric down-conversion scheme has been used to demonstrate quantum spectroscopy and imaging with undetected idler photons via measuring one-photon interference between their correlated signal beams. Recently, we considered another quantum optical measurement scheme utilizing W-type tripartite entangled signal photons that can be generated by employing three spontaneous parametric down-conversion crystals and by inducing coherences or path-indistinguishabilities between their correlated idler beams and between quantum vacuum fields. Here, we consider an extended triple stimulated parametric down-conversion scheme for quantum optical measurement of sample properties with undetected idler and photons. Noting the real effect of vacuum field indistinguishability on the fringe visibility as well as the role of zero-point field energy in the interferometry, we show that this scheme is an ideal and efficient way to create a coherent state of W-type entangled signal photons. We anticipate that this scheme would be of critical use in further developing quantum optical measurements in spectroscopy and microscopy with undetected photons.

DOI
10.1063/1.5029297

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Parametric down-conversion is a second-order nonlinear optical process annihilating a pump photon and creating a pair of photons in the signal and idler modes. Then, by using two parametric down-converters and introducing a path indistinguishability for the two generated idler modes, a quantum coherence between two conjugate signal beams can be induced. Such a double spontaneous or stimulated parametric down-conversion scheme has been used to demonstrate quantum spectroscopy and imaging with undetected idler photons via measuring one-photon interference between their correlated signal beams. Recently, we considered another quantum optical measurement scheme utilizing W-type tripartite entangled signal photons that can be generated by employing three spontaneous parametric down-conversion crystals and by inducing coherences or path-indistinguishabilities between their correlated idler beams and between quantum vacuum fields. Here, we consider an extended triple stimulated parametric down-conversion scheme for quantum optical measurement of sample properties with undetected idler and photons. Noting the real effect of vacuum field indistinguishability on the fringe visibility as well as the role of zero-point field energy in the interferometry, we show that this scheme is an ideal and efficient way to create a coherent state of W-type entangled signal photons. We anticipate that this scheme would be of critical use in further developing quantum optical measurements in spectroscopy and microscopy with undetected photons.
Quantum spectroscopy and imaging with undetected idler photons have been demonstrated by measuring one-photon interference between the corresponding entangled signal fields from two spontaneous parametric down conversion (SPDC) crystals. In this Report, we present a new quantum optical measurement scheme utilizing three SPDC crystals in a cascading arrangement; here, neither the detection of the idler photons which interact with materials of interest nor their conjugate signal photons which do not interact with the sample is required. The coherence of signal beams in a single photon W-type path-entangled state is induced and modulated by indistinguishabilities of the idler beams and crucially the quantum vacuum fields. As a result, the optical properties of materials or objects interacting with the idler beam from the first SPDC crystal can be measured by detecting second-order interference between the signal beams generated by the other two SPDC crystals further down the set-up. This gedankenexperiment illustrates the fundamental importance of vacuum fields in generating an optical tripartite entangled state and thus its crucial role in quantum optical measurements.
Quantum spectroscopy with undetected photons (QSUP) utilizing the quantum entanglement of parametrically down-converted photons has emerged as a new spectroscopic platform. Here, we demonstrate a high-resolution and remote-measurement QSUP, where light-matter interactions and photon detections are performed in spectrally and spatially different regions. A dual-stimulated parametric down-conversion scheme with an optical frequency-comb pump and ultra-narrow coherent seed beam in an idler mode is used to generate path-entangled pairs of the undetected idler and measured frequency-comb signal photons. To demonstrate the frequency resolution of this scheme, a Fabry-Pérot cavity with a narrow bandwidth is used as a sample that modulates the distinguishability of one-photon-added coherent idler beams, which directly affects the interference fringe visibility of the entangled signal photons. We thus anticipate that the remote QSUP whose frequency resolution is determined by the linewidth of the coherent seed laser will enable the development of quantum spectroscopy featuring high resolution.
We re-examine the properties of the states produced by nondegenerate coherently stimulated parametric down-conversion wherein the signal and idler modes are seeded with coherent states of light and where the nonlinear crystal is driven by a strong classical field as described by the parametric approximation. The states produced are the two-mode squeezed coherent states defined with a specific ordering of operators, namely, the displacement operators of the two modes acting on the double vacuum state followed by the action of the two-mode squeeze operator representing the down-conversion process. Though mathematically equivalent to the reverse ordering of operators, but with different displacement parameters, the ordering we consider is closely related to what could most easily be implemented in the laboratory. The statistical properties of the state are studied with an emphasis on how they, and its average photon number, are affected by the various controllable phases, namely, those of the classical pump field of the two input coherent states. We then consider the multiphoton interference effects that arise if the two beams are overlapped on a 50:50 beam splitter, investigating the role of the phases in controlling the statistical properties of the output states. Finally, we study the prospects for the application of the states to quantum-optical interferometry to obtain sensitivities in phase-shift measurements beyond the standard quantum limit.
Coherence can be induced or stimulated in parametric down-conversion using two or three crystals when, for example, the idler modes of the crystals are aligned. Previous experiments with induced coherence [Phys. Rev. Lett. 114, 053601 (2015)] focused on which-path information and the role of vacuum fields in realizing complementarity via reduced visibility in single-photon interference. Here we describe experiments comparing induced and stimulated coherence. Different single-photon interference experiments were performed by blocking one of the pump beams in a three-crystal setup. Each counted photon is emitted from one of two crystals and which-way information may or not be available, depending on the setup. Distinctly different results are obtained in the induced and stimulated cases, especially when a variable transmission filter is inserted between the crystals. A simplified theoretical model accounts for all the experimental results and is also used to address the question of whether the phases of the signal and idler fields in parametric down-conversion are correlated.
This dissertation contains new theoretical work on how to utilize the entangled photons produced in a parametric down conversion to improve resolution and sensitivity in quantum interferometry, magnetometry and lithography. Chapter 1 introduces some basics of quantum imaging and sensing systems and gives an outline of the thesis. Chapter 2 deals with the use of entangled photons in Sagnac interferometry. We introduce the Sagnac ring interferometer and analyze the Sagnac phase shift with classical and quantum inputs of light. We compare the results obtained from entangled photon pairs input with classical and single-photon inputs. We show how the photon-photon correlation measurements increase the resolution and the sensitivity in the phase shift. In chapter three, we present an analysis of how parametric down-converted photons could be utilized in getting better spectroscopic information about a medium which has magnetic field induced anisotropy. We demonstrate how the improvement in magneto-optical rotation (MOR) of light could be realized by employing two different schemes with collinear and noncollinear down-conversion geometries compared to the use of coherent light. We calculate the resolution that can be achieved in the MOR's both by the use of coherent light and down-converted light. We discuss the possibility that the Heisenberg limit could be reached in magnetometry by the use of down-converted light. In chapter 4, we propose a new idea of using coherent beam stimulated parametric processes along with spontaneous ones to produce resolution improvement in two-photon interferometry. The stimulated processes enhance the count rate by several orders of magnitude while at the same time maintaining high visibility at large gains of the parametric process. We further find that the phases of coherent fields can also be used as tuning knobs to control the visibility of the pattern. We use coherent beams at the signal and idler frequencies as the seed light for the down-conversion process. In chapter 5, we analyze the minimum phase uncertainty of the phase measurement in a Mach-Zehnder interferometer using stimulated parametric down-conversion. We calculate the phase sensitivities for different measurement schemes. We conclude the thesis in chapter 6 and give an outlook for future work.
We study the properties of bisqueezed tripartite Gaussian states created by two spontaneous parametric down-conversion processes that share a common idler. We give a complete description of the quantum correlations across all partitions, as well as of the genuine multipartite entanglement, obtaining analytical expressions for most of the quantities of interest. We find that the state contains genuine tripartite entanglement, in addition to the bipartite entanglement among the modes that are directly squeezed. We also investigate the effect of homodyne detection of the photons in the common idler mode, and analyze the final reduced state of the remaining two signal modes. We find that this measurement leads to a conversion of the coherence of the two signal modes into entanglement, a phenomenon that can be regarded as a redistribution of quantum resources between the modes. The applications of these results to quantum optics and circuit quantum electrodynamics platforms are also discussed.