Detector Clicks Research Articles

Do(es the Influence of) Empty Waves Survive in Configuration Space?

The de Broglie–Bohm interpretation is a no-collapse interpretation, which implies that we are in principle surrounded by empty waves generated by all particles of the universe, empty waves that will never collapse. It is common to establish an analogy between these pilot-waves and 3D radio-waves, which are nearly devoided of energy but carry nevertheless information to which we may have access after an amplification process. Here we show that this analogy is limited: if we consider empty waves in configuration space, an effective collapse occurs when a detector clicks and the 3ND empty wave associated to a particle may not influence another particle (even if these two particles are identical, e.g. bosons as in the example considered here).

Detection-time distribution for several quantum particles

We address the question of how to compute the probability distribution of the time at which a detector clicks in the situation of $n$ nonrelativistic quantum particles in a volume $\mathrm{\ensuremath{\Omega}}\ensuremath{\subset}{\mathbb{R}}^{3}$ in physical space and detectors placed along the boundary $\ensuremath{\partial}\mathrm{\ensuremath{\Omega}}$ of $\mathrm{\ensuremath{\Omega}}$. We previously [Tumulka, Ann. Phys. (NY) 442, 168910 (2022)] argued in favor of a rule for the one-particle case that involves a Schr\"odinger equation with an absorbing boundary condition on $\ensuremath{\partial}\mathrm{\ensuremath{\Omega}}$ introduced by Werner; we call this rule the ``absorbing boundary rule.'' Here, we describe the natural extension of the absorbing boundary rule to the $n$-particle case. A key element of this extension is that, upon a detection event, the wave function gets collapsed by inserting the detected position, at the time of detection, into the wave function, thus yielding a wave function of $n\ensuremath{-}1$ particles. We also describe an extension of the absorbing boundary rule to the case of moving detectors.

Distribution of the time at which an ideal detector clicks

We consider the problem of computing, for a detector surface waiting for a quantum particle to arrive, the probability distribution of the time and place at which the particle gets detected, from the initial wave function of the particle in the non-relativistic regime. Although the standard rules of quantum mechanics offer no operator for the time of arrival, quantum mechanics makes an unambiguous prediction for this distribution, defined by first solving the Schrödinger equation for the big quantum system formed by the particle of interest, the detector, a clock, and a device that records the time and place of detection, then making a quantum measurement of the record at a very late time, and finally using the distribution of the recorded time and place. This leads to the question whether there is also a practical, simple rule for computing this distribution, at least approximately (i.e., for an idealized detector). We argue here in favor of a rule based on a 1-particle Schrödinger equation with a certain (absorbing) boundary condition at the ideal detecting surface, first considered by Werner in 1987. We present a novel derivation of this rule and describe how it arises as a limit of a “soft” detector represented by an imaginary potential.

Classical benchmarking of Gaussian Boson Sampling on the Titan supercomputer

Gaussian Boson Sampling is a model of photonic quantum computing where single-mode squeezed states are sent through linear-optical interferometers and measured using single-photon detectors. In this work, we employ a recent exact sampling algorithm for GBS with threshold detectors to perform classical simulations on the Titan supercomputer. We determine the time and memory resources as well as the amount of computational nodes required to produce samples for different numbers of modes and detector clicks. It is possible to simulate a system with 800 optical modes postselected on outputs with 20 detector clicks, producing a single sample in roughly two hours using $40\%$ of the available nodes of Titan. Additionally, we benchmark the performance of GBS when applied to dense subgraph identification, even in the presence of photon loss. We perform sampling for several graphs containing as many as 200 vertices. Our findings indicate that large losses can be tolerated and that the use of threshold detectors is preferable over using photon-number-resolving detectors postselected on collision-free outputs.

Bayesian estimation for quantum sensing in the absence of single-shot detection

Quantum information protocols, such as quantum error correction and quantum phase estimation, have been widely used to enhance the performance of quantum sensors. While these protocols have relied on single-shot detection, in most practical applications only an averaged readout is available, as in the case of room-temperature sensing with the electron spin associated with a nitrogen-vacancy center in diamond. Here, we theoretically investigate the application of the quantum phase estimation algorithm for high dynamic-range magnetometry, in the case where single-shot readout is not available. We show that, even in this case, Bayesian estimation provides a natural way to use the available information in an efficient way. We apply Bayesian analysis to achieve an optimized sensing protocol for estimating a time-independent magnetic field with a single electron spin associated to a nitrogen-vacancy center at room temperature and show that this protocol improves the sensitivity over previous protocols by more than a factor of 3. Moreover, we show that an extra enhancement can be achieved by considering the timing information in the detector clicks.

Reply to “Comment on ‘Null weak values and the past of a quantum particle”’

We discuss the preceding Comment and conclude that the arguments given there against the relevance of null weak values as representing the absence of a system property are not compelling. We give an example in which the transition matrix elements that make the projector weak values vanish are the same ones that suppress detector clicks in strong measurements. Whether weak values are taken to account for the past of a quantum system or not depend on general interpretional commitments of the quantum formalism itself rather than on peculiarities of the weak measurements framework.

Monitoring of quantum mode correlation functions in the presence of pointer state phase relaxation

In present work we investigate the process of interaction between two-level atom- pointer and cavity mode to obtain correlation functions of mode quantum state. In particular, we analyze the protocol of indirect photodetection which allow estimations for average values of photon number operator in any order using statistics of atom state detector clicks.

Single-particle interference only when imperfect path detectors click simultaneously

We address particle interference in a Young interferometer with observation of the path by means of imperfect detectors. With a suitably chosen reading of the imperfect detectors we find that interference would be recorded only when both path detectors click simultaneously, while the interference is completely lost when only one detector clicks. We draw as many parallels as possible with classical-optics interference.

Direct Observation of Sub-Binomial Light

Nonclassical states of light are necessary resources for quantum technologies such as cryptography, computation and the definition of metrological standards. Observing signatures of nonclassicality generally requires inferring either the photon number distribution or a quasiprobability distribution indirectly from a set of measurements. Here, we report an experiment in which the nonclassical character of families of quantum states is assessed by direct inspection of the outcomes from a multiplexed photon counter. This scheme does not register the actual photon number distribution; the statistics of the detector clicks alone serve as a witness of nonclassicality, as proposed by Sperling etal. [Phys. Rev. Lett. 109, 093601 (2012)]. Our work paves a way for the practical characterization of increasingly sophisticated states and detectors.

Calibration of single-photon detectors using quantum statistics

I show that calibration of the single-photon detector can be performed without knowledge of the signal parameters. Only partial information about the state statistics is sufficient for that. If one knows that the state is the squeezed one or the squeezed one mixed with the incoherent radiation, one can infer both the parameters of the state and the efficiency of the detector. For that one needs only to measure on/off statistics of detector clicks for the number of known absorbers placed before the detector. Thus, I suggest a scheme that performs a tomography of the signal and the measuring apparatus simultaneously.

Corpuscular Model of Two-Beam Interference and Double-Slit Experiments with Single Photons

We introduce an event-based corpuscular simulation model that reproduces the wave mechanical results of single-photon double-slit and two-beam interference experiments and (of a one-to-one copy of an experimental realization) of a single-photon interference experiment with a Fresnel biprism. The simulation comprises models that capture the essential features of the apparatuses used in the experiment, including the single-photon detectors recording individual detector clicks. We demonstrate that incorporating in the detector model, simple and minimalistic processes mimicking the memory and threshold behavior of single-photon detectors is sufficient to produce multipath interference patterns. These multipath interference patterns are built up by individual particles taking one single path to the detector where they arrive one-by-one. The particles in our model are not corpuscular in the standard, classical physics sense in that they are information carriers that exchange information with the apparatuses of the experimental set-up. The interference pattern is the final, collective outcome of the information exchanges of many particles with these apparatuses. The interference patterns are produced without making reference to the solution of a wave equation and without introducing signalling or non-local interactions between the particles or between different detection points on the detector screen.

Measuring statistical characteristics of a quantized mode in various photodetection regimes

We develop a theory of the discrete photodetection model where individual unexcited atoms from the atomic beam passing through a cavity are used as pointers. Atomic energy state selective detectors (ionization chambers) measure the escape statistics of ground-or excited-state atoms. Mandelstam’s method of successive indirect quantum measurements underlies the theory being developed. In contrast to the available works, the suggested approach takes into account the atomic beam statistics, the operation nonideality (quantum efficiencies) of ionization chambers, the detector recovery time, the back action of the probe on the quantized mode, and the relaxation process in the time interval when the cavity is empty (without atoms). We derive formulas that relate the a posteriori probabilities of photodetector clicks to the elements of the main diagonal of the initial density matrix for the cavity mode. Our numerical simulations confirm that the inverse problem of reconstructing the initial photon number distribution in a cavity can be solved using the statistics of detector clicks measured during the transient process.

Making sense of a world of clicks

In a recent article O. Ulfbeck and A. Bohr (Foundations of Physics 31, 757, 2001) have stressed the genuine fortuitousness of detector clicks, which has also been pointed out, in different terms, by the present author (American Journal of Physics 68, 728, 2000). In spite of this basic agreement, the present article raises objections to the presuppositions and conclusions of Ulfbeck and Bohr, in particular their rejection of the terminology of indefinite variables, their identification of reality with "the world of experience," their identification of experience with what takes place "on the spacetime scene," and the claim that their interpretation of quantum mechanics is "entirely liberated" from classical notions. An alternative way of making sense of a world of uncaused clicks is presented. This does not invoke experience but deals with a free-standing reality, is not fettered by classical conceptions of space and time but introduces adequate ways of thinking about the spatiotemporal aspects of the quantum world, and does not reject indefinite variables but clarifies the implications of their existence.

Theory of detection in the micromaser

The field in the micromaser cavity, the atoms which both pump and probe the micromaser, and the detectors that determine the outgoing states of the atoms are treated as a single system in order to derive a nonlinear master equation for the field in the micromaser cavity which takes the effect of undetected atoms into account. Analytic solutions for this master equation are found for both phase-insensitive and phase-sensitive detection. These solutions can be used to explicitly show the back-action effects that measurement has on the spectrum of the micromaser. In addition, these solutions are used to find analytic expressions for the mean number of successive detector clicks of the same kind as well as atom-atom and photon-photon correlation functions. In this way, the analytic solutions are linked to experimentally accessible data.

Relativistic quantum events

Standard quantum theory is inadequate to explain the mechanisms by which potential becomes actual. It is inadequate and therefore unable to describe generation of events. Niels Bohr emphasized long ago that the classical part of the world is necessary. John Bell stressed the same point: that “measurement≓ cannot even be defined within the standard quantum theory, and he sought a solution within hidden variable theories and his concept of “beables.≓ Today it is customary to try to explain emergence of the classical world through a decoherence mechanism due to “environment.≓ But, we believe, as it was with the concept of measurement, “environment≓ itself cannot be defined within the standard quantum theory. We have proposed a semiphenomenological solution to this problem by introducing explicitly, from the very beginning, classical degrees of freedom, and by coupling these degrees of freedom, through a Lindblad type coupling, to the quantum world. The resulting theory, we call “event-enhanced quantum theory.≓ EEQT allows us to describe an event-generating mechanism for individual quantum systems under continuous observation. The objections of John Bell are met and precise definitions of an “experiment≓ and of a “measurement≓ have been given within EEQT. However EEQT is, essentially, a nonrelativistic theory. In the present paper we extend the ideas of L. P. Horwitz and C. Piron and we propose a relativistic version of EEQT, with an event-generating algorithm for spin one-half particle detectors. The algorithm is based on proper time formulation of the relalivistic quantum theory. Although we use indefinite metric, all the probabilities controlling the random process of the detector clicks are nonnegative.

One-atom maser: Phase-sensitive measurements.

We reconsider a variant of the one-atom-maser setup in which the emerging atoms are probed for coherent superpositions of the two Rydberg states of the maser transition. The statistical properties of the corresponding detector clicks contain information about the temporal evolution of the phase of the quantized electromagnetic field inside the resonator. We derive analytical expressions for certain statistical quantities, such as the mean number of successive clicks of the same kind, or the atom-atom and the photon-photon correlation functions. The latter are closely related if the photon-number distribution in steady state is dominated by a single narrow peak. \textcopyright{} 1996 The American Physical Society.

Statistics of photons and de-excited atoms in a micromaser with Poissonian pumping.

Explicit expressions are derived for calculating the two-time coincidence probability density, the Mandel Q parameter of the counting statistics, and the waiting-time distribution between detector clicks for the detection of de-excited atoms leaving a micromaser with Poissonian pumping. The procedure is illustrated by applying it to the simplest trapped micromaser state for which all results can be obtained analytically. Moreover, by making use of a symmetry relation which determines the properties of the time-dependent micromaser master equation solution, it is shown that in the stationary regime for negligible thermal photon number the normalized two-time intensity correlation function of the cavity field with respect to a given time difference is equal to the normalized two-time coincidence probability density of detecting two de-excited atoms with the same time difference at the exit of the micromaser.

One-atom maser: Statistics of detector clicks.

We present a general theory for the calculation of various characteristic properties of the beam of atoms emerging from a resonator in one-atom-maser experiments. The beam is described in terms of the statistics of the detector clicks. The evolution of the state of the maser photons between clicks is governed by a nonlinear master equation. The nonlinearity originates in the necessity to account for the atoms that escape detection. Despite the permanent reductions of the photon state, resulting from the detections, the steady state of the conventional linear master equation determines the statistics of the detector clicks. The whole process is ergodic, in the sense that a single run of the experiment contains all reproducible statistical data, provided the duration of the run is much longer than all relevant correlation times. The nonlinear master equation is used to calculate the distribution of waiting times between detector clicks. Other statistical properties of the clicks that are derived include correlation functions and variances of the counting statistics. The formalism is applied to standard one-atom-maser experiments and to parity measurements on both unpumped and pumped cavities. We find that, for the standard one-atom-maser operation, none of the said statistical properties is a simple immediate indicator for a sub-Poissonian variance of the photon number. For example, the detector clicks may be antibunched although the photon distribution has a super-Poissonian variance.