High-photon-number path entanglement in the interference of spontaneously down-converted photon pairs with coherent laser light

Hofmann, Holger F.; Ono, Takafumi

doi:10.1103/physreva.76.031806

Cited by 100 publications

(105 citation statements)

References 21 publications

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“…A post-selected proof of principle experiment that employs some of these optimal states was recently performed [66]. Note that, for very low values of loss, NOON states retain their optimality [104,106], and can be approximated by states that are easy to generate [67,68]. Also, a very simple proposal based on parametric downconversion which can be realized without post-selection was proposed in [72]: it can achieve the Heisenberg bound for low loss and degrades gracefully with noise.…”

Section: Quantum Metrology With Noisementioning

confidence: 99%

“…This is possible via some rather complicated optical schemes [57][58][59][60][61] which have only been implemented in highly refined, but post-selected experiments [61][62][63][64][65][66]. However states which possess a high fidelity with the NOON states, also for large values of N , can be simply obtained by mixing a squeezed vacuum and a coherent state at a beam splitter [67][68][69]. Introducing such states at the input of a Mach-Zehnder, a scaling N −1 in the average photon number of photons employed in a given experimental run can be achieved [1].…”

Section: Applications In Quantum Interferometrymentioning

confidence: 99%

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Advances in quantum metrology

2011

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In classical estimation theory, the central limit theorem implies that the statistical error in a measurement outcome can be reduced by an amount proportional to n −1/2 by repeating the measures n times and then averaging. Using quantum effects, such as entanglement, it is often possible to do better, decreasing the error by an amount proportional to n −1 . Quantum metrology is the study of those quantum techniques that allow one to gain advantages over purely classical approaches.In this review, we analyze some of the most promising recent developments in this research field. Specifically, we deal with the developments of the theory and point out some of the new experiments. Then we look at one of the main new trends of the field, the analysis of how the theory must take into account the presence of noise and experimental imperfections.Any measurement consists in three parts: the preparation of a probe, its interaction with the system to be measured, and the probe readout. This process is often plagued by statistical or systematic errors. The source of the former can be accidental (e.g. deriving from an insufficient control of the probes or of the measured system) or fundamental (e.g. deriving from the Heisenberg uncertainty relations). Whatever their origin, we can reduce their effect by repeating the measurement and averaging the resulting outcomes. This is a consequence of the central-limit theorem: given a large number n of independent measurement results (each having a standard deviation ∆σ), their average will converge to a Gaussian distribution with standard deviation ∆σ/ √ n, so that the error scales as n −1/2 . In quantum mechanics this behavior is referred to as "standard quantum limit" (SQL) and is associated with procedures which do not fully exploit the quantum nature of the system under investigation 1 . Notably it is possible to do better when one employs quantum effects, such as entanglement among the probing devices employed for the measurements, e.g. see Refs. [1][2][3][4][5][6]. Consequently, the SQL is not a fundamental quantum mechanical bound as it can be surpassed by using "non-classical" strategies. Nonetheless, through Heisenberg-like uncertainty relations, quantum mechanics still sets ultimate limits in precision which are typically referred to as "Heisenberg bounds". In Fig. 1 we present a simple example which may be useful to un-1 In quantum optics, the n −1/2 scaling is also indicated as "shot noise", since it is connected to the discrete nature of the radiation that can be heard as "shots" in a photon counter operating in Geiger mode.derstand the quantum enhancement. Part of the emerging field of quantum technology [7], quantum metrology studies these bounds and the (quantum) strategies which allows us to attain them. More generally it deals with measurement and discrimination procedures that receive some kind of enhancement (in precision, efficiency, simplicity of implementation, etc.) through the use of quantum effects. This paper aims to review some of the most recent developmen...

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Section: Quantum Metrology With Noisementioning

confidence: 99%

Section: Applications In Quantum Interferometrymentioning

confidence: 99%

Advances in quantum metrology

2011

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“…1(a)], the probability of detecting all of the photons at a given position will display spatial fringes with a period of λ=ð2N sinðθ=2ÞÞ, where θ is the angle betweenk 1 andk 2 (assuming jk 1 j ¼ jk 2 j ¼ ð2π=λÞ). The period of the N00N fringes is N times smaller than that of classical fringes, suggesting that N00N states could be used to increase the resolution of optical systems by a factor of N. This observation has led to much subsequent work on N00N states [4,5,[13][14][15][16] and their application in tasks such as quantum lithography and quantum imaging [10][11][12]17]. However, the individual photons in the N00N state cannot be localized to better than λ=2, regardless of the narrow spatial scale of the N-photon correlation fringes [6,7].…”

mentioning

confidence: 99%

“…To generate N00N states, the relative phase between the two arms must be set to zero, and the relative amplitudes balanced. The source is optimized for N00N states of different N by simply changing the relative amplitude between the laser and DC light [15]. Ideally, two-and three-photon N00N states can be made perfectly by setting the two-photon rate from the laser equal to that from the DC light (which we will refer to as "configuration 1").…”

Section: Prl 112 223602 (2014) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

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Scalable Imaging of Superresolution

Matthews¹

2014

Physics

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N00N states-maximally path-entangled states of N photons-exhibit spatial interference patterns sharper than any classical interference pattern. This is known as superresolution. However, even given perfectly efficient number-resolving detectors, the detection efficiency of all previous measurements of such interference would decrease exponentially with the number of photons in the N00N state, often leading to the conclusion that N00N states are unsuitable for spatial measurements. A technique known as the "optical centroid measurement" has been proposed to solve this and has been experimentally verified for photon pairs; here we present the first extension beyond two photons, measuring the superresolution fringes of two-, three-, and four-photon N00N states. Moreover, we compare the N00N-state interference to the corresponding classical superresolution interference. Although both provide the same increase in spatial frequency, the visibility of the classical fringes decreases exponentially with the number of detected photons. Our work represents an essential step forward for quantum-enhanced measurements, overcoming what was believed to be a fundamental challenge to quantum metrology.

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Enhanced Phase Estimation in Parity‐Detection‐Based Mach–Zehnder Interferometer using Non‐Gaussian Two‐Mode Squeezed Thermal Input State

2023

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While the quantum metrological advantages of performing non‐Gaussian operations on two‐mode squeezed vacuum (TMSV) states have been extensively explored, similar studies in the context of two‐mode squeezed thermal (TMST) states are severely lacking. This paper explores the potential advantages of performing non‐Gaussian operations on TMST state for phase estimation using parity detection‐based Mach–Zehnder interferometry and compares it with the TMSV case. To this end, a realistic photon subtraction, addition, and catalysis model is considered. A unified Wigner function of the photon subtracted, photon added, and photon catalyzed TMST state is derived, which is used to obtain the expression for the phase sensitivity. The results show that performing non‐Gaussian operations on TMST states can enhance the phase sensitivity for significant squeezing and transmissivity parameter ranges. Because of the probabilistic nature of these operations, it is of utmost importance to consider their success probability. When the success probability is considered, the photon catalysis operation performed using a high transmissivity beam splitter is the optimal non‐Gaussian operation. This contrasts with the TMSV case, where photon addition is observed as the most optimal. Further, the derived Wigner function of the non‐Gaussian TMST states will be useful for state characterization and various quantum protocols.

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High-photon-number path entanglement in the interference of spontaneously down-converted photon pairs with coherent laser light

Cited by 100 publications

References 21 publications

Advances in quantum metrology

Advances in quantum metrology

Scalable Imaging of Superresolution

Enhanced Phase Estimation in Parity‐Detection‐Based Mach–Zehnder Interferometer using Non‐Gaussian Two‐Mode Squeezed Thermal Input State

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