Continuous-variable optical quantum-state tomography

Lvovsky, A. I.; Raymer, Michael G.

doi:10.1103/revmodphys.81.299

Cited by 1,004 publications

(1,164 citation statements)

References 235 publications

(260 reference statements)

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“…Repeating this process many times and obtaining the marginals for a large number of mechanical phase-space angles θ is sufficient to uniquely determine the mechanical quantum state of motion [35]. Quantum state tomography by measurement of the marginals was first realized with optical fields using homodyne interferometry [36] and has now become an indispensable tool in the field of quantum optics [37] being applied to other physical systems such as molecular vibration [38], spin ensembles [39], and microwave fields [40]. Here we implement such mechanical state tomography by utilizing the pulsed measurement outcome probability distribution…”

Section: Experimental Protocolmentioning

confidence: 99%

Cooling-by-measurement and mechanical state tomography via pulsed optomechanics

et al. 2013

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Observing a physical quantity without disturbing it is a key capability for the control of individual quantum systems. Such back-action-evading or quantum-non-demolition measurements were first introduced in the 1970s in the context of gravitational wave detection to measure weak forces on test masses by high precision monitoring of their motion. Now, such techniques have become an indispensable tool in quantum science for preparing, manipulating, and detecting quantum states of light, atoms, and other quantum systems. Here we experimentally perform rapid optical quantumnoise-limited measurements of the position of a mechanical oscillator by using pulses of light with a duration much shorter than a period of mechanical motion. Using this back-action evading interaction we performed both state preparation and full state tomography of the mechanical motional state. We have reconstructed mechanical states with a position uncertainty reduced to 19 pm, limited by the quantum fluctuations of the optical pulse, and we have performed 'cooling-by-measurement' to reduce the mechanical mode temperature from an initial 1100 K to 16 K. Future improvements to this technique may allow for quantum squeezing of mechanical motion, even from room temperature, and reconstruction of non-classical states exhibiting negative regions in their phase-space quasi-probability distribution.Experiments are now beginning to investigate nonclassical motion of massive mechanical devices [1][2][3]. This opens up new perspectives for quantum-physics enhanced applications and for tests of the foundations of physics. A versatile approach to manipulate mechanical states of motion is provided by the interaction with electromagnetic radiation, typically confined to microwave or optical cavities. Such cavity-optomechanics experiments [4][5][6][7][8] have thus far largely concentrated on high sensitivity continuous monitoring of the mechanical position [9][10][11][12][13][14]. Because of the back-action imparted by the probe onto the measured object, the precision of such a measurement is fundamentally constrained by the standard quantum limit (SQL) [15,16], and therefore only allows for classical phase-space reconstruction [9,17,18]. In order to observe quantum mechanical features that are smaller than the mechanical zero-point motion, backaction-evading measurement techniques that can surpass the SQL [19,20] are required. Following the early insights of Braginsky, beating the standard quantum limit 'can be achieved only in one way: design the probe so it "sees" only the measured observable ' [15]. Such backaction evading techniques were first realized for the detection of optical quadratures [21][22][23] and have since been used for, e.g. precision measurement of atomic ensemble spin [24][25][26][27][28] and quantum non-demolition microwave photon counting [29]. In optomechanics, to perform a back-action evading measurement of the mechanical position, a time-dependent measurement scheme is required. One prominent example is the so-called 'two-tone app...

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Section: Experimental Protocolmentioning

confidence: 99%

Cooling-by-measurement and mechanical state tomography via pulsed optomechanics

et al. 2013

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“…An exhaustive review of continuous variable entanglement theory can be found in a number of specialized reviews (Kok et al, 2007;Lvovsky and Raymer, 2009). Here, we briefly introduce some important quantities of entangled photon pairs, in order to later distinguish genuine entanglement from other bandwidth properties, which could also be encountered with classical light sources.…”

Section: Photon Entanglement In Multimode Statesmentioning

confidence: 99%

Nonlinear optical signals and spectroscopy with quantum light

2016

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Conventional nonlinear spectroscopy uses classical light to detect matter properties through the variation of its response with frequencies or time delays. Quantum light opens up new avenues for spectroscopy by utilizing parameters of the quantum state of light as novel control knobs and through the variation of photon statistics by coupling to matter. We present an intuitive diagrammatic approach for calculating ultrafast spectroscopy signals induced by quantum light, focusing on applications involving entangled photons with nonclassical bandwidth properties -known as "time-energy entanglement". Nonlinear optical signals induced by quantized light fields are expressed using time ordered multipoint correlation functions of superoperators in the joint field plus matter phase space. These are distinct from Glauber's photon counting formalism which use normally ordered products of ordinary operators in the field space. One notable advantage for spectroscopy applications is that entangled photon pairs are not subjected to the classical Fourier limitations on the joint temporal and spectral resolution. After a brief survey of properties of entangled photon pairs relevant to their spectroscopic applications, different optical signals, and photon counting setups are discussed and illustrated for simple multi-level model systems.

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“…Entangled photons have become an invaluable resource in quantum optics with possible applications to cryptography [1], lithography [2], metrology [3] and quantum computing [4,5]. Applications to spectroscopy received considerable attention in experiments [6][7][8][9] as well as in theoretical works [10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Photon statistics of intense entangled photon pulses

Schlawin

Mukamel

2013

J. Phys. B: At. Mol. Opt. Phys.

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Time-and frequency-gated two-photon counting is given by a four-time correlation function of the electric field. This reduces to two times with purely time gating. We calculate this function for entangled photon pulses generated by parametric down-conversion. At low intensity, the pulses consist of well-separated photon pairs, and crossover to squeezed light as the intensity is increased. This is illustrated by the two-photon absorption signal of a three-level model, which scales linearly for a weak pump intensity where both photons come from the same pair, and gradually becomes nonlinear as the intensity is increased. We find that the strong frequency correlations of entangled photon pairs persist even for higher photon numbers. This could help facilitate the application of these pulses to nonlinear spectroscopy, where these correlations can be used to manipulate congested signals.

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Continuous-variable optical quantum-state tomography

Cited by 1,004 publications

References 235 publications

Cooling-by-measurement and mechanical state tomography via pulsed optomechanics

Cooling-by-measurement and mechanical state tomography via pulsed optomechanics

Nonlinear optical signals and spectroscopy with quantum light

Photon statistics of intense entangled photon pulses

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