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arXiv:2009.11586 · Physical Review A

Poissonian twin-beam states and the effect of symmetrical photon subtraction in loss estimations

N. Samantaray, Jonathan C. F. Matthews, John Rarity

Published Dec 27, 2021• 2 citations
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Abstract

We have devised an experimentally realizable model generating twin-beam states whose individual beam photon statistics are varied from thermal to Poissonian (by temporal mode averaging) keeping the nonclassical mode correlation intact. We have studied the usefulness of these states for loss measurement by considering three different estimators, comparing with the correlated thermal twin-beam states generated from spontaneous parametric down conversion or four-wave mixing. We then incorporated the photon subtraction operation into the model and demonstrated their performance in loss estimations with respect to unsubtracted states at both fixed squeezing and per photon exposure of the absorbing sample. For instance, at fixed squeezing, for two photon subtraction, up to three times advantage is found. An unexpected result in the latter case is that in some operating regimes the photon subtraction scheme can also give up to $20%$ advantage over the correlated thermal beam result and no advantages are obtained when the statistics of each beam turns to Poissonian. We have also made a comparative study of these estimators for finding the best measurement for loss estimations. We present results for all the values of the model parameters changing the statistics of twin-beam states from thermal to Poissonian.

DOI
10.1103/physreva.104.063718

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We have devised an experimentally realizable model generating twin-beam states whose individual beam photon statistics are varied from thermal to Poissonian (by temporal mode averaging) keeping the nonclassical mode correlation intact. We have studied the usefulness of these states for loss measurement by considering three different estimators, comparing with the correlated thermal twin-beam states generated from spontaneous parametric down conversion or four-wave mixing. We then incorporated the photon subtraction operation into the model and demonstrated their performance in loss estimations with respect to unsubtracted states at both fixed squeezing and per photon exposure of the absorbing sample. For instance, at fixed squeezing, for two photon subtraction, up to three times advantage is found. An unexpected result in the latter case is that in some operating regimes the photon subtraction scheme can also give up to 2020%20 advantage over the correlated thermal beam result and no advantages are obtained when the statistics of each beam turns to Poissonian. We have also made a comparative study of these estimators for finding the best measurement for loss estimations. We present results for all the values of the model parameters changing the statistics of twin-beam states from thermal to Poissonian.
We have studied theoretical un-symmetric multi-photon subtracted twin beam state and demonstrated a method for generating states that resembles to high photon number states with the increase in the number of subtracted photons through Wigner distribution function, which can be reconstructed experimentally by Homodyne measurement. A crucial point is high non-classicality is obtained by photon subtraction when mean photons per mode of twin beam state is low. We have calculated photon statistics from the phase space distribution function and found sub-poissonian behaviour in the same low mean photons regime. Furthermore, we have tested the usefulness of such states for realistic absorption measurement including detection losses by computing quantum Fisher-Information from measured Wigner function after interaction the sample. We have compared the performance of these states with respect to coherent and demonstrated how the quantum advantage is related to non-classical enhancement. We presented results up to three photon subtraction which show remarkable quantum advantage over both initial thermal and coherent state reaching the ultimate quantum limit in the loss estimation.
Multiple photon addition and subtraction applied to multi-mode thermal and sub-Poissonian fields as well as twin beams are mutually compared using one experimental setup. Twin beams (TWBs) with tight spatial correlations detected by an intensified CCD camera with high spatial resolution are used to prepare the initial fields. Up to three photons are added or subtracted to arrive at the nonclassical and non-Gaussian states. Only the photon-subtracted thermal states (TSs) remain classical. In general, the experimental photon-added states exhibit greater nonclassicality and non-Gaussianity than the comparable photon-subtracted states. Once photons are added or subtracted in twin beams, both processes result in comparable properties of the obtained states owing to twin-beam photon pairing.
Compound beams composed of simple experimental blocks (detected in simultaneous detection windows) that form specific quantum-correlated structures are suggested for simulating the properties of different quantum operations used for creating highly nonclassical and entangled multi-mode states needed in quantum communication, metrology, and information protocols. Qualitative and quantitative comparison of multi-photon addition and subtraction in compound multi-mode thermal as well as sub-Poissonian beams and multi-mode twin beams with their intensities extending over two orders in magnitude is provided. Adding and subtracting up to twenty photocounts, optimal conditions for the generation of experimental nonclassical states are identified. In general, photon addition is identified as advantageous over photon subtraction for the multi-mode thermal and sub-Poissonian beams: It induces (enhances) the nonclassicality in the former (latter) state. Contrary to this, photon subtraction outperforms photon addition in the multi-mode twin beams. Moreover, exploiting temporal photon-pair correlations in compound twin beams when post-selecting, nearly ideal experimental photon(s) addition is demonstrated. The results apply for the beams with mean photon number per mode much less than one.
The accuracy of optical measurements at low light levels is limited by the quantum noise of the source and by the random nature of the interaction with the measured object. The source noise may be reduced by use of nonclassical photon-number squeezed light. We consider the use of two photon-correlated beams (generated, for example, by spontaneous parametric downconversion) to measure the optical transmittance of an object. The photons of each beam obey a random Poisson process but are synchronized in time. One beam is used to probe the object, and the other is used as a reference providing information on the realization of the random arrival of photons at the object. The additional information available by such measurement may be exploited to improve the accuracy of the measurement. Various estimators, including the maximum-likelihood estimator, are considered, and their performance is evaluated and compared with the measurement based on a single-beam conventional (Poissonian) source and a maximally squeezed (fixed-photon-number) source. The performance advantage that is established depends on parameters such as the intensity of the source, the transmittance of the object, the quantum efficiency of the detectors, the background noise, and the degree of correlation of the photon numbers in the two beams.
Using the method of photon addition into both beams of a multi-mode twin beam, a new kind of highly nonclassical states is obtained. As these states exhibit tight photon-number cross-correlations and are endowed with marginal sub-Poissonian photon-number distributions, we suggest to call them sub-Poissonian twin beams. We reveal their properties in the model as well as experimentally using mesoscopic twin beams. An intensified CCD camera as a photon-number resolving detector is applied to prepare as well as characterize the states with up to three photons added into each beam and containing from 2.8 to 7.5 photons in average in each beam. Their nonclassicality as well as non-Gaussianity are determined to demonstrate their prominent features. Spatial correlations of photons in the beams are exploited to improve the properties of the generated states. The beams are promising as the quantum light source for virtual-state entangled-photon spectroscopy. Their properties are prospective for monitoring and manipulating two-photon light–matter interactions.
Two-beam states obtained by partial photon-number-resolving detection in one beam of a multi-mode twin beam are experimentally investigated using an intensified CCD camera. In these states, sub-Poissonian photon-number distributions in one beam are accompanied by sub-shot-noise fluctuations in the photon-number difference of both beams. Multi-mode character of the twin beam implying the beam nearly Poissonian statistics is critical for reaching sub-Poissonian photon-number distributions, which contrasts with the use of a two-mode squeezed vacuum state. Relative intensities of both nonclassical effects as they depend on the generation conditions are investigated both theoretically and experimentally using photon-number distributions of these fields. Fano factor, noise-reduction parameter, local and global nonclassicality depths, degree of photon-number coherence, mutual entropy as a non-Gaussianity quantifier, and negative quasi-distributions of integrated intensities are used to characterize these fields. Spatial photon-pair correlations as means for improving the field properties are employed. These states are appealing for quantum metrology and imaging including the virtual-state entangled-photon spectroscopy.