The final goal of quantum hypothesis testing is to achieve quantum advantage over all possible classical strategies. In the protocol of quantum reading this advantage is achieved for information retrieval from an optical memory, whose generic cell stores a bit of information in two possible lossy channels. For this protocol, we show, theoretically and experimentally, that quantum advantage is obtained by practical photon-counting measurements combined with a simple maximum-likelihood decision. In particular, we show that this receiver combined with an entangled two-mode squeezed vacuum source is able to outperform any strategy based on statistical mixtures of coherent states for the same mean number of input photons. Our experimental findings demonstrate that quantum entanglement and simple optics are able to enhance the readout of digital data, paving the way to real applications of quantum reading and with potential applications for any other model that is based on the binary discrimination of bosonic loss.
The protocol of quantum reading refers to the quantum enhanced retrieval of information from an optical memory, whose generic cell stores a bit of information in two possible lossy channels. In the following we analyze the case of a particular class of optical receiver, based on photon counting measurement, since they can be particularly simple in view of real applications. We show that a quantum advantage is achievable when a transmitter based on two-mode squeezed vacuum (TMSV) states is combined with a photon counting receiver, and we experimentally confirm it. In this paper, after introduci…
We show that nature imposes no fundamental upper limit to the number of information bits per expended photon that can, in principle, be read reliably when classical data is encoded in a medium that can only passively modulate the amplitude and phase of the probe light. We show that with a coherent-state (laser) source, an on-off (amplitude-modulation) pixel encoding, and shot-noise-limited direct detection (an overly-optimistic model for commercial CD/DVD drives), the highest photon information efficiency achievable in principle is about 0.5 bit per transmitted photon. We then show that a cohe…
Resources for the manipulation and measurements of high-dimensional photonic signals are crucial for implementing qu$d$it-based applications. Here we propose potentially high-performance, chip-compatible devices for such purposes by exploiting quantum-frequency conversion in nonlinear optical media. Specifically, by using sum-frequency generation in a $χ^{(2)}$ waveguide we show how mode-resolved photon counting can be accomplished for telecom-band photonic signals subtending multiple temporal modes. Our method is generally applicable to any nonlinear medium with arbitrary dispersion property.
We analyze a simultaneous continuous measurement of photon-counting and homodyne detection. The stochastic master equation or stochastic Schrödinger equation describing the measurement process includes both jump-type and diffusive-type stochastic increments. Analytic expressions of the wave function conditioned on homodyne and photon-counting records are obtained, yielding the probability density distributions and generating functions of the measurement records. Formula for the expectation values of the homodyne records conditioned on a photon-counting event is also derived which quantitativel…
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.
We consider the phase sensing via weak optical coherent state at quantum limit precision. A new detection scheme for the phase estimation is proposed which is inspired by the suboptimal quantum measurement in coherent optical communication. We theoretically analyze a performance of our detection scheme, which we call the displaced-photon counting, for phase sensing in terms of the Fisher information and show that the displaced-photon counting outperforms the static homodyne and heterodyne detections in wide range of the target phase. The proof-of-principle experiment is performed with linear o…
We demonstrate a photon-counting optical time-domain reflectometry with 42.19 dB dynamic range using an ultra-low noise up-conversion single photon detector. By employing the long wave pump technique and a volume Bragg grating, we reduce the noise of our up-conversion single photon detector, and achieve a noise equivalent power of -139.7 dBm/sqrt(Hz). We perform the OTDR experiments using a fiber of length 216.95 km, and show that our system can identify defects along the entire fiber length with a distance resolution better than 10 cm in a measurement time of 13 minutes.
Spontaneous downconversion is a versatile source for correlated biphotons that has been employed in many quantum sensing and imaging experiments. Spatially-resolved photon-counting detectors allow to access a large number of modes, posing the challenge of an accurate description of such systems. We propose a simple model to generate images as though acquired by a photon-counting camera, and allow to simulate and characterise the detection of quantum correlations. We derive quantitative parameters characteristic of the spatial correlations for a given experiment, comparing the images produced b…
We study the accuracy of determining the phase space quasidistribution of a single quantized light mode by a photon counting experiment. We derive an exact analytical formula for the error of the experimental outcome. This result provides an estimation for the experimental parameters, such as the number of events, required to determine the quasidistribution with assumed precision. Our analysis also shows that it is in general not possible to compensate the imperfectness of the photodetector in a numerical processing of the experimental data. The discussion is illustrated with Monte Carlo simul…
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.
We demonstrate niobium titanium nitride superconducting nanowires patterned on stoichiometric silicon nitride waveguides for detecting visible and infrared photons. The use of silicon nitride on insulator on silicon substrates allows us to simultaneously realize photonic circuits for visible and infrared light and integrate them with nanowire detectors directly on-chip. By implementing a traveling wave detector geometry in this material platform, we achieve efficient single photon detection for both wavelength regimes. Our detectors are an ideal match for integrated quantum optics as they prov…
Optically measuring in the photon counting regime is a recurrent challenge in modern physics and a guarantee to develop weakly invasive probes. Here we investigate this idea on a hybrid nano-optomechanical system composed of a nanowire hybridized to a single Nitrogen-Vacancy (NV) defect. The vibrations of the nanoresonator grant a spatial degree of freedom to the quantum emitter and the photon emission event can now vary in space and time. We investigate how the nanomotion is encoded on the detected photon statistics and explore their spatio-temporal correlation properties. This allows a quant…
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…
Coherent multidimensional optical spectroscopy techniques are broadly applied across the electromagnetic spectrum ranging from NMR to the UV. These reveal properties of matter through correlation plots of signal fields generated in response to sequences of short pulses with variable delays. Here we discuss a new class of multidimensional techniques obtained by time-and-frequency resolved photon coincidence counting measurements of N photons which constitutes a 2N dimensional spectrum. A compact description of these signals is developed based on time ordered superoperators rather than the norma…
Quantum nondemolition (QND) measurements of photons is a much pursued endeavor in the field of quantum optics and quantum information processing. Here we propose a novel hybrid optoelectromechanical platform that integrates a cavity system with a hybrid electromechanical probe for QND photon counting. Building upon a mechanical-mode-mediated nonperturbative electro-optical dispersive coupling, our protocol performs the QND photon counting measurement by means of the current-voltage characteristics of the probe. In particular, we show that the peak voltage shift of the differential conductance …
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.
We consider a basic model of digital memory where each cell is composed of a reflecting medium with two possible reflectivities. By fixing the mean number of photons irradiated over each memory cell, we show that a non-classical source of light can retrieve more information than any classical source. This improvement is shown in the regime of few photons and high reflectivities, where the gain of information can be surprising. As a result, the use of quantum light can have non-trivial applications in the technology of digital memories, such as optical disks and barcodes.
We consider a basic model of digital memory where each cell is composed of a reflecting medium with two possible reflectivities. By fixing the mean number of photons irradiated over each memory cell, we show that a non-classical source of light can retrieve more information than any classical source. This improvement is shown in the regime of few photons and high reflectivities, where the gain of information can be surprising. As a result, the use of quantum light can have non-trivial applications in the technology of digital memories, such as optical disks and barcodes.
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 experimentally study Bragg-scattering four-wave mixing in a highly nonlinear fiber at telecom wavelengths using photon counters. We explore the polarization dependence of this process with a continuous wave signal in the macroscopic and attenuated regime, with a wavelength shift of 23 nm. Our measurements of mean photon numbers per second under various pump polarization configurations agree well with the theoretical and numerical predictions based on classical models. We discuss the impact of noise under these different polarization configurations.
We consider the use of single-photon counting detectors in coherence-domain imaging. Detectors operated in this mode exhibit reduced noise, which leads to increased sensitivity for weak light sources and weakly reflecting samples. In particular, we experimentally demonstrate the possibility of using superconducting single-photon detectors (SSPDs) for optical coherence-domain reflectometry (OCDR). These detectors are sensitive over the full spectral range that is useful for carrying out such imaging in biological samples. With counting rates as high as 100 MHz, SSPDs also offer a high rate of d…
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.
We present a linearly arrayed, 16-element, superconducting nanowire single-photon detector with 83.4$\%$ system detection efficiency at 1550 nm and a mean per-element dead-time of 9.6-ns, enabling counting at 1 giga-count per second with $>50\%$ System Detection Efficiency. This device was designed and fabricated in an existing scalable commercial process.
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…
We show that detection of single photons is not subject to the fundamental limitations that accompany quantum linear amplification of bosonic mode amplitudes, even though a photodetector does amplify a few-photon input signal to a macroscopic output signal. Alternative limits are derived for \emph{nonlinear} photon-number amplification schemes with optimistic implications for single-photon detection. Four commutator-preserving transformations are presented: one idealized (which is optimal) and three more realistic (less than optimal). Our description makes clear that nonlinear amplification ta…
We demonstrate fast counting and multiphoton detection abilities of a Silicon Photo Multiplier (SiPM). In fast counting mode we are able to detect two consecutive photons separated by only 2.3 ns corresponding to 430 MHz. The counting efficiency for small optical intensities at a wavelength of 532 nm was found to be around 8.3% with a dark count rate of 50 kHz at T=-7 degrees Celsius. Using the SiPM in multiphoton detection mode, we find a good signal discrimination for different numbers of simultaneous detected photons.
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…
A direct-detection Brillouin optical time-domain reflectometry (BOTDR) is proposed and demonstrated by using an up-conversion single-photon detector and a fiber Fabry-Perot scanning interferometer (FFP-SI). Taking advantage of high signal-to-noise ratio of the detector and high spectrum resolution of the FFP-SI, the Brillouin spectrum along a polarization maintaining fiber (PMF) is recorded on a multiscaler with a small data size directly. In contrast with conventional BOTDR adopting coherent detection, photon-counting BOTDR is simpler in structure and easier in data processing. In the demonst…
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…
We theoretically study cooperative effects in the steady-state transmission of photons through a medium of $N$ radiators. Using methods from quantum transport, we find a cross-over in scaling from $N$ to $N^2$ in the current and even higher powers of $N$ in the higher cumulants of the photon counting statistics as a function of the tunable source occupation. The effect should be observable for atoms confined within a nano-cell with a pumped optical cavity as photon source.
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…
The mechanism of extraction of information stored in a quantum memory is studied here in detail. We consider memories containing a single excitation of a collective atomic state, which is mapped into a single photon during the reading process. A theory is developed for the wavepacket of the extracted photon, leading to a simple analytical expression depending on the key parameters of the problem, like detuning and intensity of the read field and the number of atoms in the atomic ensemble. This theory is then compared to a large set of experimental situations and a satisfactory quantitative agr…
We investigate two different kinds of quantum trajectories for a nonlinear photon resonator subject to two-photon pumping, a configuration recently studied for the generation of photonic Schroedinger cat states. In the absence of feedback control and in the strong-driving limit, the steady-state density matrix is a statistical mixture of two states with equal weight. While along a single photon-counting trajectory the systems intermittently switches between an odd and an even cat state, we show that upon homodyne detection the situation is different. Indeed, homodyne quantum trajectories revea…
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 analyze the full counting statistics of photons emitted by a double quantum dot (DQD) coupled to a high-quality microwave resonator by electric dipole interaction. We show that at the resonant condition between the energy splitting of the DQD and the photon energy in the resonator, photon statistics exhibits both a sub-Poissonian distribution and antibunching. In the ideal case, when the system decoherence stems only from photodetection, the photon noise is reduced below one-half of the noise for the Poisson distribution and is consistent with current noise. The photon distribution remains …
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…
When a mesoscopic conductor is coupled to a high-quality electromagnetic cavity the flow of charges and the flux of photons leaking out of the cavity can both depend strongly on the coupled quantum dynamics of the system. Using a voltage-biased Josephson junction as a model system, we demonstrate that there is a simple connection between the full counting statistics of the charges and the photons in the long time limit. We then reveal the intimate relation between the counting statistics and the nonlinear dynamics of the system, uncovering novel regimes of coherent charge and photon transport …
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 provide the optimal strategy for unambiguous quantum reading of optical memories, namely when perfect retrieving of information is achieved probabilistically, for the case where noise and loss are negligible. We describe the experimental quantum optical implementations, and provide experimental results for the single photon case.
