Multipath Interferometers Research Articles

Counterfactuality, back-action, and information gain in multi-path interferometers

The presence of an absorber in one of the paths of an interferometer changes the output statistics of that interferometer in a fundamental manner. Since the individual quantum particles detected at any of the outputs of the interferometer have not been absorbed, any non-trivial effect of the absorber on the distribution of these particles over these paths is a counterfactual effect. Here, we quantify counterfactual effects by evaluating the information about the presence or absence of the absorber obtained from the output statistics, distinguishing between classical and quantum counterfactual effects. We identify the counterfactual gain which quantifies the advantage of quantum counterfactual protocols over classical counterfactual protocols, and show that this counterfactual gain can be separated into two terms: a semi-classical term related to the amplitude blocked by the absorber, and a Kirkwood-Dirac quasiprobability assigning a joint probability to the blocked path and the output port. A negative Kirkwood-Dirac term between a path and an output port indicates that inserting the absorber into that path will have a focussing effect, increasing the probability of particles arriving at that output port, resulting in a significant enhancement of the counterfactual gain. We show that the magnitude of quantum counterfactual effects cannot be explained by a simple removal of the absorbed particles, but originates instead from a well-defined back-action effect caused by the presence of the absorber in one path, on particles in other paths.

Multilevel atomic Ramsey interferometry for precise parameter estimations* *Project supported by the National Natural Science Foundation of China (Grant No. 11974290).

Multi-path (or multi-mode) entanglement has been proved to be a useful resource for sub-shot-noise sensitivity of phase estimation, which has aroused much research interest inquantum metrology recently. Various schemes of multi-path interferometers based on optical systems have been put forward. Here, we study a multi-state interferometer with multi-level atoms by projective measurements. Specifically, we investigate its ultimate sensitivity described by quantum Fisher information theory and find that the Cramer–Rao bound can be achieved. In particular, we investigate a specific scheme to improve the sensitivityof magnetometery with a three-state interferometry delivered by a single nitrogen-vacancy (NV) center of diamond with tailor pulses. The impacts of imperfections of the atomic beam-splitter, described by the three-level quantum Fourier transform, on the sensitivity of phase estimation is also discussed.

A generalized multipath delayed-choice experiment on a large-scale quantum nanophotonic chip

Bohr’s complementarity is one central tenet of quantum physics. The paradoxical wave-particle duality of quantum matters and photons has been tested in Young’s double-slit (double-path) interferometers. The object exclusively exhibits wave and particle nature, depending measurement apparatus that can be delayed chosen to rule out too-naive interpretations of quantum complementarity. All experiments to date have been implemented in the double-path framework, while it is of fundamental interest to study complementarity in multipath interferometric systems. Here, we demonstrate generalized multipath wave-particle duality in a quantum delayed-choice experiment, implemented by large-scale silicon-integrated multipath interferometers. Single-photon displays sophisticated transitions between wave and particle characters, determined by the choice of quantum-controlled generalized Hadamard operations. We characterise particle-nature by multimode which-path information and wave-nature by multipath coherence of interference, and demonstrate the generalisation of Bohr’s multipath duality relation. Our work provides deep insights into multidimensional quantum physics and benchmarks controllability of integrated photonic quantum technology.

Dispersion cancellation in a quantum interferometer with independent single photons.

A key technique to perform proper quantum information processing is to get a high visibility quantum interference between independent single photons. One of the crucial elements that affects the quantum interference is a group velocity dispersion that occurs when single photons pass through a dispersive medium. We theoretically and experimentally demonstrate that an effect of group velocity dispersion on the two-photon interference can be cancelled if two independent single photons experience the same amount of pulse broadening. This dispersion cancellation effect can be applied to a multi-path linear interferometer with multiple independent single photons. As multi-path quantum interferometers are at the heart of quantum communication, photonic quantum computing, and boson sampling applications, our work should find wide applicability in quantum information science.

Simulation of wave-particle duality in multipath interferometers on a quantum computer

We present an architecture to investigate wave-particle duality in $N$-path interferometers on a universal quantum computer involving as low as $2\log N$ qubits and develop a measurement scheme which allows the efficient extraction of quantifiers of interference visibility and which-path information. We implement our algorithms for interferometers with up to $N=16$ paths in proof-of-principle experiments on a noisy intermediate-scale quantum (NISQ) device using down to $\mathcal{O}(\log N)$ gates and despite increasing noise consistently observe a complementary behavior between interference visibility and which-path information. Our results are in accordance with our current understanding of wave-particle duality and allow its investigation for interferometers with an exponentially growing number of paths on future quantum devices beyond the NISQ era.

Experimental demonstration of tight duality relation in three-path interferometer**Project supported by the National Key Research and Development Program of China (Grant Nos. 2016YFA0302700 and 2017YFA0304100), the National Natural Science Foundation of China (Grant Nos. 11822408, 11674304, 11774335, 61490711, 11474267, 11821404, 11325419, 11904356, and 91321313), the Youth Innovation Promotion Association, Chinese Academy of Sciences (Grant No. 2017492), the Foundation for Scientific

Bohr’s principle of complementarity has a long history and it is an important topic in quantum theory, among which the famous example is the duality relation. The relation between visibility C and distinguishability D, , has long been recognized as the only representative of the duality relation. However, recent researches have shown that this inequality is not good enough because it is not tight for multipath interferometers. Meanwhile, a tight bound for the multipath interferometer has been put forward. Here we design and experimentally implement a three-path interferometer coupling with path indicator states. The wave property of photons is characterized by l1-norm coherence measure, and the particle property is based on distinguishability of the indicator states. The new duality relation of the three-path interferometer is demonstrated in our experiment, which bounds the union of a right triangle and a part of elliptical area inside the quadrant of a unit circle. Data analysis confirms that the new bound is tight for photons in three-path interferometers.

Quasicontinuous-Variable Quantum Computation with Collective Spins in Multipath Interferometers.

Collective spins of large atomic samples trapped inside optical resonators can carry quantum information that can be processed in a way similar to quantum computation with continuous variables. It is shown here that by combining the resonators in multipath interferometers one can realize coupling between different samples, and that polynomial Hamiltonians can be constructed by repeated spin rotations and twisting induced by dispersive interaction of the atoms with light. Application can be expected in the efficient simulation of quantum systems.

Entropic framework for wave-particle duality in multipath interferometers

An interferometer - no matter how clever the design - cannot reveal both the wave and particle behavior of a quantum system. This fundamental idea has been captured by inequalities, so-called wave-particle duality relations (WPDRs), that upper bound the sum of the fringe visibility (wave behavior) and path distinguishability (particle behavior). Another fundamental idea is Heisenberg's uncertainty principle, stating that some pairs of observables cannot be known simultaneously. Recent work has unified these two principles for two-path interferometers. Here we extend this unification to $n$-path interferometers, showing that WPDRs correspond to a modern formulation of the uncertainty principle stated in terms of entropies. Furthermore, our unification provides a framework for solving an outstanding problem of how to formulate universally valid WPDRs for interferometers with more than two paths, and we employ this framework to derive some novel WPDRs.

Multipath interferometer with ultracold atoms trapped in an optical lattice

We study an ultra-cold gas of $N$ bosons trapped in a one dimensional $M$-site optical lattice perturbed by a spatially dependent potential $g\cdot x^j$, where the unknown coupling strength $g$ is to be estimated. We find that the measurement uncertainty is bounded by $\Delta g\propto\frac1{N (M^j-1)}$. For a typical case of a linear potential, the sensitivity improves as $M^{-1}$, which is a result of multiple interferences between the sites -- an advantage of multi-path interferometers over the two-mode setups. Next, we calculate the estimation sensitivity for a specific measurement where, after the action of the potential, the particles are released from the lattice and form an interference pattern. If the parameter is estimated by a least-square fit of the average density to the interference pattern, the sensitivity still scales like $M^{-1}$ for linear potentials and can be further improved by preparing a properly correlated initial state in the lattice.

Factorization algorithm based on the periodicity measurement of a CTES

We introduce a new factorization algorithm based on the measurement of the periodicity of a determined function, similar to Shor's algorithm. In particular, such a function is given by a generalized continuous truncated exponential sum (CTES). The CTES interference pattern satisfies a remarkable scaling property, which allows one to plot the interferogram as a function of a suitable continuous variable depending on the number to factorize. This allows one, in principle, to factorize arbitrary numbers with a single interferogram. In particular, information about the factors is encoded in the location of the interference maxima, which repeat periodically in the interferogram. A possible analogue computer for the implementation of such an algorithm can be realized using multi-path optical interferometers, with polychromatic light sources and a high-resolution spectrometer. The experimental accuracy in the realization of the CTES interferogram and the bandwidth of the polychromatic sources determine the largest number Nmax factorable. Once the CTES interferogram is recorded, all the numbers with value up to Nmax can be factorable, without performing any further measurement.

Scheme for implementing atomic multiport devices

Multiport generalizations of beam splitters are the key component in multipath interferometers, which are important in a range of quantum state engineering and precision measurement schemes. Here we propose a straightforward method for implementing multiport devices for atoms trapped in optical ring lattices. These devices are interesting as atoms have certain properties (such as mass) that photons do not, and the ring configuration makes them useful for applications such as precision gyroscopes. We discuss how they could be employed in useful measurement schemes and investigate how practical considerations limit the size of the devices that can be achieved by this method.

WAVE-PARTICLE DUALITY IN MULTI-PATH INTERFEROMETERS: GENERAL CONCEPTS AND THREE-PATH INTERFEROMETERS

For two-path interferometers, the which-path predictability [Formula: see text] and the fringe visibility [Formula: see text] are familiar quantities that are much used to talk about wave-particle duality in a quantitative way. We discuss several candidates that suggest themselves as generalizations P of [Formula: see text] for multi-path interferometers, and treat the case of three paths in considerable detail. To each choice for the path knowledge P, the interference strength V — the corresponding generalization of [Formula: see text] — is found by a natural, operational procedure. In experimental terms, it amounts to finding those equal-weight superpositions of the path amplitudes which maximize P for the emerging intensities. Mathematically speaking, one needs to identify a certain optimum one among the Fourier transforms of the state of the interfering quantum object. Wave-particle duality is manifest, inasmuch as P = 1 implies V = 0 and V = 1 implies P = 0, whatever definition is chosen. The possible values of the pair (P,V) are restricted to an area with corners at (P,V) = (0,0), (P,V) = (1,0), and (P,V) = (0,1), with the shape of the border line from (1,0) to (0,1), depending on the particular choice for P and the induced definition of V.

Source coherence impairments in a direct detection direct sequence optical code-division multiple-access system

We demonstrate that direct sequence optical code- division multiple-access (DS-OCDMA) encoders and decoders using sampled fiber Bragg gratings (S-FBGs) behave as multipath interferometers. In that case, chip pulses of the prime sequence codes generated by spreading in time-coherent data pulses can result from multiple reflections in the interferometers that can superimpose within a chip time duration. We show that the autocorrelation function has to be considered as the sum of complex amplitudes of the combined chip as the laser source coherence time is much greater than the integration time of the photodetector. To reduce the sensitivity of the DS-OCDMA system to the coherence time of the laser source, we analyze the use of sparse and nonperiodic quadratic congruence and extended quadratic congruence codes.

Fourier multiport devices

A formalism for multiport devices is developed in which the creation and annihilation operators at the output are related with those at the input through a finite Fourier transform. By considering two specific inputs of number states and coherent states, we show how these devices can be used to produce multimode Schroedinger cat states and can be combined to create multipath interferometers. We introduce uncertainty relations for the distributions of particles in the input modes and the correlations between the output modes. These allow us to determine how the phase resolution of the output state scales with the number of ports and particles. This scaling is of fundamental interest for schemes that seek to use multipath interferometers for enhanced measurement precision.

Information-theoretic approach to single-particle and two-particle interference in multipath interferometers.

We propose entropic measures for the strength of single-particle and two-particle interference in interferometric experiments where each particle of a pair traverses a multipath interferometer. Optimal single-particle interference excludes any two-particle interference, and vice versa. We report an inequality that states the compromises allowed by quantum mechanics in intermediate situations, and identify a class of two-particle states for which the upper bound is reached. Our approach is applicable to symmetric two-partite systems of any finite dimension.

Working standard of wavelength unit for pulsed laser

Finding it necessary to include a metrological circuitry for means of measurement of pulsed laser wavelength, a working standard and standard and working means of measurements of the pulsed laser wavelengths were designed and built. The working standard (WS) is designed to transfer the wavelength unit to the standard lasers and the standard means of measurement. The design of the WS is described. The WS of the wavelength unit for pulsed lasers was developed based on multipath Fizeau interferometers with an automatic system for processing of measurement information.