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Runyon MT, Nacke CH, Sit A, Granados-Baez M, Giner L, Lundeen JS. Implementation of nearly arbitrary spatially varying polarization transformations: an in-principle lossless approach using spatial light modulators. Appl Opt 2018; 57:5769-5778. [PMID: 30118046 DOI: 10.1364/ao.57.005769] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2018] [Accepted: 06/09/2018] [Indexed: 06/08/2023]
Abstract
A fast and automated scheme for general polarization transformations holds great value in adaptive optics, quantum information, and virtually all applications involving light-matter and light-light interactions. We present an experiment that uses a liquid crystal on silicon spatial light modulator to perform polarization transformations on a light field. We experimentally demonstrate the point-by-point conversion of uniformly polarized light fields across the wavefront to realize arbitrary, spatially varying polarization states. Additionally, we demonstrate that a light field with an arbitrary spatially varying polarization can be transformed to a spatially invariant (i.e., uniform) polarization.
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2
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Thekkadath GS, Saaltink RY, Giner L, Lundeen JS. Determining Complementary Properties with Quantum Clones. Phys Rev Lett 2017; 119:050405. [PMID: 28949711 DOI: 10.1103/physrevlett.119.050405] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/04/2017] [Indexed: 06/07/2023]
Abstract
In a classical world, simultaneous measurements of complementary properties (e.g., position and momentum) give a system's state. In quantum mechanics, measurement-induced disturbance is largest for complementary properties and, hence, limits the precision with which such properties can be determined simultaneously. It is tempting to try to sidestep this disturbance by copying the system and measuring each complementary property on a separate copy. However, perfect copying is physically impossible in quantum mechanics. Here, we investigate using the closest quantum analog to this copying strategy, optimal cloning. The coherent portion of the generated clones' state corresponds to "twins" of the input system. Like perfect copies, both twins faithfully reproduce the properties of the input system. Unlike perfect copies, the twins are entangled. As such, a measurement on both twins is equivalent to a simultaneous measurement on the input system. For complementary observables, this joint measurement gives the system's state, just as in the classical case. We demonstrate this experimentally using polarized single photons.
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Affiliation(s)
- G S Thekkadath
- Department of Physics, Centre for Research in Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - R Y Saaltink
- Department of Physics, Centre for Research in Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - L Giner
- Department of Physics, Centre for Research in Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - J S Lundeen
- Department of Physics, Centre for Research in Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
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Lundeen JS, McCall WV, Rumble M, Krystal A, Case D, Benca R, Looney SW. 0715 SELECTING FUNCTIONAL DATA ANALYSIS SUMMARY MEASURES OF SLEEP ACTIGRAPHY DATA TO REFLECT CLINICAL MORNINGNESS/EVENINGNESS. Sleep 2017. [DOI: 10.1093/sleepj/zsx050.714] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
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4
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Thekkadath GS, Giner L, Chalich Y, Horton MJ, Banker J, Lundeen JS. Direct Measurement of the Density Matrix of a Quantum System. Phys Rev Lett 2016; 117:120401. [PMID: 27689255 DOI: 10.1103/physrevlett.117.120401] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/26/2016] [Indexed: 06/06/2023]
Abstract
One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements since it requires a global reconstruction. Here, we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.
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Affiliation(s)
- G S Thekkadath
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - L Giner
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - Y Chalich
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - M J Horton
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - J Banker
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
| | - J S Lundeen
- Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, 25 Templeton Street, Ottawa, Ontario K1N 6N5, Canada
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Bamber C, Sutherland B, Patel A, Stewart C, Lundeen JS. Measurement of the transverse electric field profile of light by a self-referencing method with direct phase determination. Opt Express 2012; 20:2034-2044. [PMID: 22330444 DOI: 10.1364/oe.20.002034] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We present a method for measuring the transverse electric field profile of a beam of light which allows for direct phase retrieval. The measured values correspond, within a normalization constant, to the real and imaginary parts of the electric field in a plane normal to the direction of propagation. This technique represents a self-referencing method for probing the wavefront characteristics of light.
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Affiliation(s)
- C Bamber
- INMS, National Research Council of Canada 1200 Montreal Rd, M-36, Ottawa, K1A 0R6 Canada.
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6
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Abstract
We study both experimentally and theoretically the generation of photon pairs by spontaneous four-wave mixing (SFWM) in standard birefringent optical fibers. The ability to produce a range of two-photon spectral states, from highly correlated (entangled) to completely factorable, by means of cross-polarized birefringent phase matching, is explored. A simple model is developed to predict the spectral state of the photon pair which shows how this can be adjusted by choosing the appropriate pump bandwidth, fiber length and birefringence. Spontaneous Raman scattering is modeled to determine the tradeoff between SFWM and background Raman noise, and the predicted results are shown to agree with experimental data.
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Affiliation(s)
- Brian J Smith
- Centre for Quantum Technologies, National University of Singapore 3 Science Drive 2, 117543 Singapore, Singapore.
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7
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Worsley AP, Coldenstrodt-Ronge HB, Lundeen JS, Mosley PJ, Smith BJ, Puentes G, Thomas-Peter N, Walmsley IA. Absolute efficiency estimation of photon-number-resolving detectors using twin beams. Opt Express 2009; 17:4397-4411. [PMID: 19293867 DOI: 10.1364/oe.17.004397] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
A nonclassical light source is used to demonstrate experimentally the absolute efficiency calibration of a photon-number-resolving detector. The photon-pair detector calibration method developed by Klyshko for single-photon detectors is generalized to take advantage of the higher dynamic range and additional information provided by photon-number-resolving detectors. This enables the use of brighter twin-beam sources including amplified pulse pumped sources, which increases the relevant signal and provides measurement redundancy, making the calibration more robust.
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Affiliation(s)
- A P Worsley
- University of Oxford, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, United Kingdom
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8
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Dorner U, Demkowicz-Dobrzanski R, Smith BJ, Lundeen JS, Wasilewski W, Banaszek K, Walmsley IA. Optimal quantum phase estimation. Phys Rev Lett 2009; 102:040403. [PMID: 19257407 DOI: 10.1103/physrevlett.102.040403] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2008] [Revised: 11/03/2008] [Indexed: 05/27/2023]
Abstract
By using a systematic optimization approach, we determine quantum states of light with definite photon number leading to the best possible precision in optical two-mode interferometry. Our treatment takes into account the experimentally relevant situation of photon losses. Our results thus reveal the benchmark for precision in optical interferometry. Although this boundary is generally worse than the Heisenberg limit, we show that the obtained precision beats the standard quantum limit, thus leading to a significant improvement compared to classical interferometers. We furthermore discuss alternative states and strategies to the optimized states which are easier to generate at the cost of only slightly lower precision.
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Affiliation(s)
- U Dorner
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
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Lundeen JS, Steinberg AM. Experimental joint weak measurement on a photon pair as a probe of Hardy's paradox. Phys Rev Lett 2009; 102:020404. [PMID: 19257252 DOI: 10.1103/physrevlett.102.020404] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2008] [Indexed: 05/27/2023]
Abstract
It has been proposed that the ability to perform joint weak measurements on postselected systems would allow us to study quantum paradoxes. These measurements can investigate the history of those particles that contribute to the paradoxical outcome. Here we experimentally perform weak measurements of joint (i.e., nonlocal) observables. In an implementation of Hardy's paradox, we weakly measure the locations of two photons, the subject of the conflicting statements behind the paradox. Remarkably, the resulting weak probabilities verify all of these statements but, at the same time, resolve the paradox.
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Affiliation(s)
- J S Lundeen
- Department of Physics, University of Toronto, 60 St. George Street, Toronto ON, M5S 1A7, Canada
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10
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Garay-Palmett K, McGuinness HJ, Cohen O, Lundeen JS, Rangel-Rojo R, U'ren AB, Raymer MG, McKinstrie CJ, Radic S, Walmsley IA. Photon pair-state preparation with tailored spectral properties by spontaneous four-wave mixing in photonic-crystal fiber. Opt Express 2007; 15:14870-14886. [PMID: 19550766 DOI: 10.1364/oe.15.014870] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
We study theoretically the generation of photon pairs by spontaneous four-wave mixing (SFWM) in photonic crystal optical fiber. We show that it is possible to engineer two-photon states with specific spectral correlation ("entanglement") properties suitable for quantum information processing applications. We focus on the case exhibiting no spectral correlations in the two-photon component of the state, which we call factorability, and which allows heralding of single-photon pure-state wave packets without the need for spectral post filtering. We show that spontaneous four wave mixing exhibits a remarkable flexibility, permitting a wider class of two-photon states, including ultra-broadband, highly-anticorrelated states.
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Resch KJ, Puvanathasan P, Lundeen JS, Mitchell MW, Bizheva K. Classical dispersion-cancellation interferometry. Opt Express 2007; 15:8797-804. [PMID: 19547215 DOI: 10.1364/oe.15.008797] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
Even-order dispersion cancellation, an effect previously identified with frequency-entangled photons, is demonstrated experimentally for the first time with a linear, classical interferometer. A combination of a broad bandwidth laser and a high resolution spectrometer was used to measure the intensity correlations between anti-correlated optical frequencies. Only 14% broadening of the correlation signal is observed when significant material dispersion, enough to broaden the regular interferogram by 4250%, is introduced into one arm of the interferometer.
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Mitchell MW, Lundeen JS, Steinberg AM. Super-resolving phase measurements with a multiphoton entangled state. Nature 2004; 429:161-4. [PMID: 15141206 DOI: 10.1038/nature02493] [Citation(s) in RCA: 160] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2003] [Accepted: 03/16/2004] [Indexed: 11/10/2022]
Abstract
Interference phenomena are ubiquitous in physics, often forming the basis of demanding measurements. Examples include Ramsey interferometry in atomic spectroscopy, X-ray diffraction in crystallography and optical interferometry in gravitational-wave studies. It has been known for some time that the quantum property of entanglement can be exploited to perform super-sensitive measurements, for example in optical interferometry or atomic spectroscopy. The idea has been demonstrated for an entangled state of two photons, but for larger numbers of particles it is difficult to create the necessary multiparticle entangled states. Here we demonstrate experimentally a technique for producing a maximally entangled three-photon state from initially non-entangled photons. The method can in principle be applied to generate states of arbitrary photon number, giving arbitrarily large improvement in measurement resolution. The method of state construction requires non-unitary operations, which we perform using post-selected linear-optics techniques similar to those used for linear-optics quantum computing.
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Affiliation(s)
- M W Mitchell
- Department of Physics, University of Toronto, 60 St George Street, Toronto, Ontario M5S 1A7, Canada.
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Mohseni M, Lundeen JS, Resch KJ, Steinberg AM. Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm. Phys Rev Lett 2003; 91:187903. [PMID: 14611316 DOI: 10.1103/physrevlett.91.187903] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2002] [Revised: 07/21/2003] [Indexed: 05/24/2023]
Abstract
For a practical quantum computer to operate, it is essential to properly manage decoherence. One important technique for doing this is the use of "decoherence-free subspaces" (DFSs), which have recently been demonstrated. Here we present the first use of DFSs to improve the performance of a quantum algorithm. An optical implementation of the Deutsch-Jozsa algorithm can be made insensitive to a particular class of phase noise by encoding information in the appropriate subspaces; we observe a reduction of the error rate from 35% to 7%, essentially its value in the absence of noise.
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Affiliation(s)
- M Mohseni
- Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, Canada, M5S 1A7
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14
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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.
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Affiliation(s)
- K J Resch
- Department of Physics, University of Toronto, 60 St. George Street, Toronto ON M5S 1A7, Canada
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15
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Abstract
We demonstrate suppression and enhancement of spontaneous parametric down-conversion via quantum interference with two weak fields from a local oscillator (LO). Effectively, pairs of LO photons up-convert with high efficiency for appropriate phase settings, exhibiting an effective nonlinearity enhanced by at least 10 orders of magnitude. This constitutes a two-photon switch and promises to be applicable to a wide variety of quantum nonlinear optical phenomena.
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Affiliation(s)
- K J Resch
- Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, Canada M5S 1A7
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