We demonstrate a comparison of different multiplexing architectures based on quantum detector tomography. Using the purity of their measurement outcomes, we gain insight about the photon-number resolving power of the devices. Further, we calculate the information each measurement outcome can extract out of a Hilbert space with given dimension. Our work confirms that more multiplexing outcomes enable higher photon-number resolving power; however, the splitting between those outcomes must be optimized as well.
By virtue of density operator's P-representation in the coherent state representation, we derive a new quantum mechanical photon counting distribution formula. As its application, we find the photon counting distribution for the pure squeezed state relates to the Legendre function, which seems a new result.
Recently, a non-Gaussian state, which is called cubic phase state has been experimentally realized. In this work we show that, in case one has access to a proper cubic phase state, it is possible to make photon counting experiments and generate extremely squeezed states.
Bases of exactly localized Minkowski and Rindler states on spacelike hypersurfaces are used to describe inertial and accelerated photon counting devices. It is found that the spacetime coordinates of photons absorbed by a pair of counteraccelerating detectors in causally disconnected Rindler wedges are correlated. If a photon is absorbed by a single accelerated detector the Minkowski vacuum collapses to a state containing at least one photon and that photon can be absorbed by an inertial detector.
We implement a photon-counting Optical Time Domain Reflectometer (OTDR) at 1.55um which exhibits a high 2-point resolution and a high accuracy. It is based on a low temporal-jitter photon-counting module at 1.55um. This detector is composed of a periodically poled Lithium niobate (PPLN) waveguide, which provides a wavelength conversion from near infrared to visible light, and a low jitter silicon photon-counting detector. With this apparatus, we obtain centimetre resolution over a measurement range of tens of kilometres.
Experimental reconstructions of photon number distributions of both continuous-wave and pulsed light beams are reported. Our scheme is based on on/off avalanche photodetection assisted by maximum-likelihood estimation and does not involve photon counting. Reconstructions of the distribution for both semiclassical and quantum states of light are reported for single-mode as well as for multimode beams.
Single-photon detection and photon counting play a central role in a large number of quantum communication and computation protocols. While the efficiency of state-of-the-art photo-detectors is well below the desired limits, quantum state measurements in trapped ions can be carried out with efficiencies approaching 100%. Here, we propose a method that can in principle achieve ideal photon counting, by combining the techniques of photonic quantum memory and ion-trap fluorescence detection: after mapping the quantum state of a propagating light pulse onto metastable collective excitations of a t…
The performance of nondeterministic nonlinear gates in linear optics relies on the photon counting scheme being employed and the efficiencies of the detectors in such schemes. We assess the performance of the nonlinear sign gate, which is a critical component of linear optical quantum computing, for two standard photon counting methods: the double detector array and the visible light photon counter. Our analysis shows that the double detector array is insufficient to provide the photon counting capability for effective nondeterministic nonlinear transformations, and we determine the gate fidel…
We show how to obtain the photon distribution of a single-mode field using only avalanche photodetectors. The method is based on measuring the field at different quantum efficiencies and then inferring the photon distribution by maximum-likelihood estimation. The convergence of the method and its robustness against fluctuations are illustrated by means of numerically simulated experiments.
Dehmelt's Lambda-experiment for a three-level atom with simultaneously driven strong and weak transition is studied within quantum stochastic calculus approach. The statistics of the emitted photons is found by the method of generating functional of the corresponding two dimensional output counting process. In particular, the average waiting times for a count are calculated.
The behavior of an atomic double lambda system in the presence of a strong off-resonant classical field and a few-photon resonant quantum field is examined. It is shown that the system possesses properties that allow a single-photon state to be distilled from a multi-photon input wave packet. In addition, the system is also capable of functioning as an efficient photodetector discriminating between one- and two-photon wave packets with arbitrarily high efficiency.
Although universal continuous-variable quantum computation cannot be achieved via linear optics (including squeezing), homodyne detection and feed-forward, inclusion of ideal photon counting measurements overcomes this obstacle. These measurements are sometimes described by arrays of beam splitters to distribute the photons across several modes. We show that such a scheme cannot be used to implement ideal photon counting and that such measurements necessarily involve nonlinear evolution. However, this requirement of nonlinearity can be moved "off-line," thereby permitting universal continuous-…
We compare the principles and experimental results of two different QPSK signal detection configurations, photon counting and super homodyning, for applications in fiber-optic Quantum Key Distribution (QKD) systems operating at telecom wavelength, using the BB84 protocol.
We investigate the implementation of binary projective measurements with linear optics. This problem can be viewed as a single-shot discrimination of two orthogonal pure quantum states. We show that any two orthogonal states can be perfectly discriminated using only linear optics, photon counting, coherent ancillary states, and feedforward. The statement holds in the asymptotic limit of large number of these physical resources.
Photon counting measurements are analyzed for obtaining a classical phase parameter in linear Mach Zehnder interferometer (MZI), by the use of phase estimation theories. The detailed analysis is made for four cases: a) Coherent states inserted into the interferometer. b) Fock number state inserted in one input port of the interferometer and the vacuum into the other input port. c) Coherent state inserted into one input port of the interferometer and squeezed-vacuum state in the other input port. d) Exchanging the first beam-splitter (BS1) of a MZI by a non-linear system which inserts a NOON st…
The physical parameters governing the dynamics of a light emitting quantum system can be estimated from the photon counting signal. The information available in the full detection record can be analysed by means of the distribution of waiting times between detection events. Our theory allows calculation of the asymptotic, long time behaviour of the sensitivity limit, and it applies to emission processes with branching towards different final states accompanied by the emission of distinguishable photons. We illustrate the theory by application to a laser driven $Λ$-type atom.
Detection of radiation signals is at the heart of precision metrology and sensing. In this article we show how the fluctuations in photon counting signals can be exploited to optimally extract information about the physical parameters that govern the dynamics of the emitter. For a simple two-level emitter subject to photon counting, we show that the Fisher information and the Cramér- Rao sensitivity bound based on the full detection record can be evaluated from the waiting time distribution in the fluorescence signal which can, in turn, be calculated for both perfect and imperfect detectors by…
The uses of a silicon-pixel camera with very good time resolution ($\sim$nanosecond) for detecting multiple, bunched optical photons is explored. We present characteristics of the camera and describe experiments proving its counting capabilities. We use a spontaneous parametric down-conversion source to generate correlated photon pairs, and exploit the Hong-Ou-Mandel interference effect in a fiber-coupled beam splitter to bunch the pair onto the same output fiber. It is shown that the time and spatial resolution of the camera enables independent detection of two photons emerging simultaneously…
Thermal (or pseudo-thermal) radiation has been recently proposed for imaging and interference types of experiments to simulate entangled states. We report an experimental study on the momentum correlation properties of a pseudo-thermal field in the photon counting regime. The characterization and understanding of such a light source in the context of two photon physics, especially its similarities and differences compared to entangled two-photon states, is useful in gaining knowledge of entanglement and may help us to assess the real potential of applications of chaotic light in this context.
Number-resolving single-photon detectors represent a key technology for a host of quantum optics protocols, but despite significant efforts, state-of-the-art devices are limited to few photons. In contrast, state-dependent atom counting in arrays can be done with extremely high fidelity up to hundreds of atoms. We show that in waveguide QED, the problem of photon counting can be reduced to atom counting, by entangling the photonic state with an atomic array in the collective number basis. This is possible as the incoming photons couple to collective atomic states and can be achieved by enginee…
We present experimental results on a method to perform polarimetry on ensembles of single photons. Our setup is based on a measurement method known to be optimal for estimating the state of two level systems. The setup has no moving parts and is sensitive to weak sources (emitting single photons) of light as it relies on photon counting and has potential applications in both classical polarization measurements and quantum communication scenarios. In our implementation, we are able to reconstruct the Stokes parameters of pure polarization states with an average fidelity of 99.9%.
We propose a design for a photon counting detector capable of resolving multiphoton events. The basic element of the setup is a fiber loop, which traps the input field with the help of a fast electrooptic switch. A single weakly coupled avalanche photodiode is used to detect small portions of the signal field extracted from the loop. We analyze the response of the loop detector to an arbitrary input field, and discuss both the reconstruction of the photon number distribution of an unknown field from the count statistics measured in the setup, and the application of the detector in conditional …
We give detailed insight into photon counting OTDR (nu-OTDR) operation, ranging from Geiger mode operation of avalanche photodiodes (APD), analysis of different APD bias schemes, to the discussion of OTDR perspectives. Our results demonstrate that an InGaAs/InP APD based nu-OTDR has the potential of outperforming the dynamic range of a conventional state-of-the-art OTDR by 10 dB as well as the 2-point resolution by a factor of 20. Considering the trace acquisition speed of nu-OTDRs, we find that a combination of rapid gating for high photon flux and free running mode for low photon flux is the…
The relaxation of a quantum field stored in a high-$Q$ superconducting cavity is monitored by non-resonant Rydberg atoms. The field, subjected to repetitive quantum non-demolition (QND) photon counting, undergoes jumps between photon number states. We select ensembles of field realizations evolving from a given Fock state and reconstruct the subsequent evolution of their photon number distributions. We realize in this way a tomography of the photon number relaxation process yielding all the jump rates between Fock states. The damping rates of the $n$ photon states ($0\leq n \leq 7$) are found …
Coherent optical fibre networks are extremely sensitive to thermal, mechanical and acoustic noise, which requires elaborate schemes of phase stabilization with dedicated auxiliary lasers, multiplexers and photodetectors. This is particularly demanding in quantum networks operating at the single-photon level. Here we propose a simple method of phase stabilization based on single-photon counting and apply it to quantum fibre networks implementing single-photon interference on a lossless beamsplitter and coherent perfect absorption on a metamaterial absorber. As a proof of principle, we show diss…
We report a direct measurement of the Wigner function characterizing the quantum state of a light mode. The experimental scheme is based on the representation of the Wigner function as an expectation value of a displaced photon number parity operator. This allowed us to scan the phase space point-by-point, and obtain the complete Wigner function without using any numerical reconstruction algorithms.
We show, in the context of single photon detection, that an atomic three-level model for a transmon in a transmission line does not support the predictions of the nonlinear polarisability model known as the cross-Kerr effect. We show that the induced displacement of a probe in the presence or absence of a single photon in the signal field, cannot be resolved above the quantum noise in the probe. This strongly suggests that cross-Kerr media are not suitable for photon counting or related single photon applications. Our results are presented in the context of a transmon in a one dimensional micr…
We report a procedure to detect mid-infrared single photons at 4.65 um via a two-stage scheme based on Sum Frequency Generation, using a Periodically Poled Lithium Niobate (PPLN) nonlinear crystal and a Silicon Avalanche Photodiode. An experimental investigation shows that, in addition to a high timing resolution, this technique yields a detection sensitivity of 1.24 pW with 63mW of net pump power.
We address photon-number-assisted, polarization- based, binary communication systems equipped with photon counting receivers. In these channels information is encoded in the value of polarization phase-shift but the carrier has and additional degree of freedom, i.e. its photon distribution, which may be exploited to implement binary input-multiple output (BIMO) channels also in the presence of a phase-diffusion noise affecting the polarization. Here we analyze the performances of these channels, which approach capacity by means of iteratively decoded error correcting codes. In this paper we us…
A high efficiency method for the generation of correlated photon pairs accompanied by a reliable means to characterize the efficiency of that process is needed in the study of correlated photon pairs and entangled states involving more than three photons, which have important potential applications in quantum information and quantum communication. In this study, we report the first characterization of the efficiency of generation of correlated photon pairs emitted from a CuCl single crystal using the biexciton-resonance hyper-parametric scattering (RHPS) method which is the highly efficient me…
We derived quantum trajectories for a system interacting with the environment prepared in a continuous mode single photon state as the limit of discrete filtering model with an environment defined as series of independent qubits prepared initially in the entangled state being an analogue of a continuous mode state. The environment qubits interact with the quantum system and they are subsequently measured. The initial correlation between the bath qubits is the source of the non-Markovianity. The conditional evolutions of the quantum system for limit of the continuous in time observations togeth…
In this work we present a large-deviation analysis for the counting statistics of atomic spontaneous emissions continuously detected in finite-bandwidth non-Markovian environment. We show that the statistics of the spontaneous emissions depends on the response time of the detector, which can result in big differences such as dynamical phase transition. This feature excludes the idea of regarding the spontaneous emissions as detection-free objective events. Possible experiment is briefly discussed in connection with the state-of-the-art optical cavity set-up.
We show how the same set-up and procedure, exploiting spatially multi-mode quantum correlations, allows the absolute calibration of a EMCCD camera from the analog regime down to the single photon counting level, just by adjusting the brightness of the quantum source. At single photon level EMCCD can be operated as an on-off detector, where quantum efficiency depends on the discriminating threshold. We develop a simple model to explain the connection of the two different regime demonstrating that the efficiency estimated in the analog (bright) regime allows to accurately predict the detector be…
Determining an unknown quantum state from an ensemble of identical systems is a fundamental, yet experimentally demanding, task in quantum science. Here we study the number of measurement bases needed to fully characterize an arbitrary multi-mode state containing a definite number of photons, or an arbitrary mixture of such states. We show this task can be achieved using only linear optics and photon counting, which yield a practical though non-universal set of projective measurements. We derive the minimum number of measurement settings required and numerically show that this lower bound is s…
The performance of three types of InGaAs/InP avalanche photodiodes is investigated for photon counting at 1550 nm in the temperature range of thermoelectric cooling. The best one yields a dark count probability of $% 2.8\cdot 10^{-5}$ per gate (2.4 ns) at a detection efficiency of 10% and a temperature of -60C. The afterpulse probability and the timing jitter are also studied. The results obtained are compared with those of other papers and applied to the simulation of a quantum key distribution system. An error rate of 10% would be obtained after 54 kilometers.
We present an InGaAs/InP avalanche photodiode with an active quenching circuit on an ASIC (application specific integrated circuit) that is capable of operating in both gated and free-running modes. The 1.6mm2 ASIC chip is fabricated using CMOS (complementary metal oxide semiconductor) technology guaranteeing long-term stability, reliability and compactness. In the free-running mode we find a single photon detection efficiency of 10% with <2kHz of noise.
We present a general model to account for the multimode nature of the quantum electromagnetic field in projective photon-counting measurements. We focus on photon-subtraction experiments, where non-gaussian states are produced conditionally. These are useful states for continuous-variable quantum information processing. We present a general method called mode reduction that reduces the multimode model to an effective two-mode problem. We apply this method to a multimode model describing broadband parametric downconversion, thereby improving the analysis of existing experimental results. The ma…
We propose a simple and efficient method for generating metrologically useful quantum entanglement in an ensemble of spin-1 atoms that interacts with a high-finesse optical cavity mode. It requires straightforward preparation of $N$ atoms in the $m_F=0$ sublevel, tailoring of the atom-field interaction to give an effective Tavis-Cummings model for the collective spin-1 ensemble, and a photon counting measurement on the cavity output field. The photon number provides a projective measurement of the collective spin length $S$, which, for the chosen initial state, is heavily weighted around value…
It is well known that a minimum error quantum measurement for arbitrary binary optical coherent states can be realized by a receiver that comprises interfering with a coherent reference light, photon counting, and feedback control. We show that, for ternary optical coherent states, a minimum error measurement cannot always be realized by such a receiver. The problem of finding an upper bound on the maximum success probability of such a receiver can be formulated as a convex programming. We derive its dual problem and numerically find the upper bound. At least for ternary phase-shift keyed cohe…
We derive a closed photo-counting formula, including noise counts and a finite quantum efficiency, for photon number resolving detectors based on on-off detectors. It applies to detection schemes such as array detectors and multiplexing setups. The result renders it possible to compare the corresponding measured counting statistics with the true photon number statistics of arbitrary quantum states. The photo-counting formula is applied to the discrimination of photon numbers of Fock states, squeezed states, and odd coherent states. It is illustrated for coherent states that our formula is indi…
Joint photocount distributions of a weak twin beam acquired by an iCCD camera are analyzed with respect to the beam spatial correlations. A method for extracting these correlations from the experimental joint photocount distributions is suggested using a suitable statistical model that quantifies the contribution of spatial correlations to the joint photocount distributions. In detail, the profile of twin-beam intensity spatial cross-correlation function is revealed from the curve that gives the genuine mean photon-pair number (both photons from a pair are detected) as a function of the extent…
Polarized light microscopy using path-entangled $N$-photon states (i.e., the N00N states) has been demonstrated to surpass the shot-noise limit at very low light illumination. However, the microscopy images suffer from divergence of phase sensitivity, which inevitably reduces the image quality. Here, we show that due to experimental imperfections, such a singularity also takes place in the microscopy that uses twin-Fock states of light for illumination. We propose two schemes to completely eliminate this singularity: (i) locking the phase shift sensed by the beams at the optimal working point,…
We present a method to classically enhance noise-robustness of single-pixel imaging in photon counting regime with a pulsed source. By using time-domain cross-correlations between temporal profiles of a pulsed source and received signals, our scheme classically imitates the noise rejection concept of quantum imaging. Under a strong noise environment in which the background noise intensity is up to 120 times higher than the signal one, we compare three different images obtained by conventional, quantum-enhanced, and classically enhanced schemes. The results show that the classically enhanced sc…
Loophole-free Bell tests are essential if one wishes to perform device-independent quantum key distribution (QKD), since any loophole could be used by a potential adversary to undermine the security of the protocol. Crucial work by Eberhard demonstrated that weakly entangled two-qubit states have a far greater resistance to the detection loophole than maximally entangled states, allowing one to close the loophole with detection efficiency greater than 2/3. Here we demonstrate that this same limit holds for photon-counting CHSH Bell tests which can demonstrate non-locality for higher dimensiona…
We present a scheme for a photon-counting detection system that can be operated at incident photon rates higher than otherwise possible by suppressing the effects of detector deadtime. The method uses an array of N detectors and a 1-by-N optical switch with a control circuit to direct input light to live detectors. Our calculations and models highlight the advantages of the technique. In particular, using this scheme, a group of N detectors provides an improvement in operation rate that can exceed the improvement that would be obtained by a single detector with deadtime reduced by 1/N, even if…
We suggest a scheme of using two-mode squeezed vacuum for conditional teleportation of quantum states of optical field. Alice mixes the input state with one of the squeezed modes on another squeezing device and detects the output photon numbers. The result is then communicated to Bob who shifts the photon number of his part accordingly. This is a principally realizable modification of the recent scheme [G.J. Milburn and S.L. Braunstein, Phys. Rev. A 60, 937 (1999)] where measurements of photon number difference and phase sum are considered. We show that for some classes of states this method c…
We study GHZ-type and W-type three-mode entangled coherent states. Both the types of entangled coherent states violate Mermin's version of the Bell inequality with threshold photon detection (i.e., without photon counting). Such an experiment can be performed using linear optics elements and threshold detectors with significant Bell violations for GHZ-type entangled coherent states. However, to demonstrate Bell-type inequality violations for W-type entangled coherent states, additional nonlinear interactions are needed. We also propose an optical scheme to generate W-type entangled coherent st…
Optomechanical systems are rapidly becoming one of the most promising platforms for observing quantum behaviour, especially at the macroscopic level. Moreover, thanks to their state-of-the-art methods of fabrication, they may now enter regimes of non-linear interactions between their constituent mechanical and optical degrees of freedom. In this work, we show how this novel opportunity may serve to construct a new generation of optomechanical sensors. We consider the canonical optomechanical setup with the detection scheme being based on time-resolved counting of photons leaking from the cavit…
Probabilities of photon counts at the output of a multiport optical device are generalised for optical sources of arbitrary quantum states in partially distinguishable optical modes. For the single-mode photon sources, the generating function for the probabilities is a linear combination of the matrix permanents of positive semi-definite Hermitian matrices, where each Hermitian matrix is a Hadamard product of a submatrix of the multiport matrix and a Hermitian matrix describing partial distinguishability. For the multi-mode sources the generating function is given by an integral of the Husimi …
Time development of electromagnetic fields in closed cavities under continuous detection of photons continues to be a subject of confusing controversy. Recently Dodonov et al. [Phys. Rev. A, 75, 013806, 2007] argued that their model of quantum superoperators (E model) invalidates some of the predictions of the previously introduced photon counting model of Srinivas and Davies [J. Mod. Optic. 28, 981, 1981] (SD model). Both the SD and the E models are based on two postulated quantum jump superoperators: (1) the one-count operator corresponding to the absorption of a single photon and (2) the no…
The key requirement for harnessing the quantum properties of light is the capability to detect and count individual photons. Of particular interest are photon-number-resolving detectors, which allow one to determine whether a state of light is classical or genuinely quantum. Existing schemes for addressing this challenge rely on a proportional conversion of photons to electrons. As such, they are capable of correctly characterizing small photon fluxes, yet are limited by uncertainties in the conversion rate. In this work, we employ a divide-and-conquer approach to overcome these limitations by…
We investigate the possibility of implementing a given projection measurement using linear optics and arbitrarily fast feedforward based on the continuous detection of photons. In particular, we systematically derive the so-called Dolinar scheme that achieves the minimum error discrimination of binary coherent states. Moreover, we show that the Dolinar-type approach can also be applied to projection measurements in the regime of photonic-qubit signals. Our results demonstrate that for implementing a projection measurement with linear optics, in principle, unit success probability may be approa…
In quantum computation with continous-variable systems, quantum advantage can only be achieved if some non-Gaussian resource is available. Yet, non-Gaussian unitary evolutions and measurements suited for computation are challenging to realize in the lab. We propose and analyze two methods to apply a polynomial approximation of any unitary operator diagonal in the amplitude quadrature representation, including non-Gaussian operators, to an unknown input state. Our protocols use as a primary non-Gaussian resource a single-photon counter. We use the fidelity of the transformation with the target …
The ability to coherently control mechanical systems with optical fields has made great strides over the past decade, and now includes the use of photon counting techniques to detect the non-classical nature of mechanical states. These techniques may soon be used to perform an opto-mechanical Bell test, hence highlighting the potential of cavity opto-mechanics for device-independent quantum information processing. Here, we propose a witness which reveals opto-mechanical entanglement without any constraint on the global detection efficiencies in a setup allowing one to test a Bell inequality. W…
We apply the formalism of quantum measurement theory to the idealized measurement of the position of a particle with an optical interferometer, finding that the backaction of counting entangled photons systematically collapses the particle's wavefunction toward a narrow Gaussian wavepacket at the location $x_\mathrm{est}$ determined by the measurement without appeal to environmental decoherence or other spontaneous collapse mechanism. Further, the variance in the particle's position, as calculated from the post-measurement wavefunction agrees precisely with shot-noise limited uncertainty of th…
