Phase measurement using a lossless Mach-Zehnder interferometer with certain entangled $N$-photon states can lead to a phase sensitivity of the order of 1/N, the Heisenberg limit. However, previously considered output measurement schemes are different for different input states to achieve this limit. We show that it is possible to achieve this limit just by the parity measurement for all the commonly proposed entangled states. Based on the parity measurement scheme, the reductions of the phase sensitivity in the presence of photon loss are examined for the various input states.
Sub-picosecond coincidence timing from nonlocal intensity interference of entangled photons allows quantum interferometry for plasmas. Using a warm plasma dispersion relation, we correlate phase measurement sensitivity with different plasma properties or physics mechanisms over 6 orders of magnitude. Due to $N^α$ ($α\leq -1/2$) scaling with the photon number $N$, quantum interferometry using entangled light can probe small signals in plasmas not previously accessible. As an example, it is predicted that plasmas will induce shifts to a Gaussian dip, a well-known quantum optics phenomenon that i…
We study two different decoherence modes for entangled qubits by considering a Liouville - von Neumann master equation. Mode A is determined by projection operators onto the eigenstates of the Hamiltonian and mode B by projectors onto rotated states. We present solutions for general and for Bell diagonal states and calculate for the later the mixedness and the amount of entanglement given by the concurrence. We propose a realization of the decoherence modes within neutron interferometry by applying fluctuating magnetic fields. An experimental test of the Kraus operator decomposition describing…
A quantum gravity-gradiometer consists of two spatially separated ensembles of atoms interrogated by pulses of a common laser beam. Laser pulses cause the probability amplitudes of atomic ground-state hyperfine levels to interfere, producing two motion-sensitive phase shifts which allow the measurement of the average acceleration of each ensemble, and, via simple differencing, of the acceleration gradient. Here I propose entangling the quantum states of the two ensembles prior to the pulse sequence, and show that entanglement encodes their relative acceleration in a single interference phase w…
Many quantum advantages in metrology and communication arise from interferometric phenomena. Such phenomena can occur on ultrafast time scales, particularly when energy-time entangled photons are employed. These have been relatively unexplored as their observation necessitates time resolution much shorter than conventional photon counters. Integrating nonlinear optical gating with conventional photon counters can overcome this limitation and enable subpicosecond time resolution. Here, using this technique and a Franson interferometer, we demonstrate high-visibility quantum interference with tw…
Implications of field quantization on Ramsey interferometry are discussed and general conditions for the occurrence of interference are obtained. Interferences do not occur if the fields in two Ramsey zones have precise number of photons. However in this case we show how two atom (like two photon) interferometry can be used to discern a variety of interference effects as the two independent Ramsey zones get entangled by the passage of first atom. Generation of various entangled states like |0,2>+|2,0> are discussed and in far off resonance case generation of entangled state of two coherent sta…
Recent progress in generating entangled spin states of neutral atoms provides opportunities to advance quantum sensing technology. In particular, entanglement can enhance the performance of accelerometers and gravimeters based on light-pulse atom interferometry. We study the effects of error sources that may limit the sensitivity of such devices, including errors in the preparation of the initial entangled state, imperfections in the laser pulses, momentum spread of the initial atomic wave packet, measurement errors, spontaneous emission, and atom loss. We determine that, for each of these err…
We introduce a general scheme of many-particle interferometry in which two identical sources are used and "which-way information" is eliminated by making the paths of one or more particles identical (path identity). The scheme allows us to generate many-particle entangled states. We provide general forms of these states and show that they can be expressed as superpositions of various Dicke states. We illustrate cases in which the scheme produces maximally entangled two-qubit states (Bell states) and maximally three-tangled states (three-particle Greenberger-Horne-Zeilinger-class states). A str…
Even though ideas of extracting future-related, or Faster-Than-Light (FTL) information from hyperspace using quantum entanglement have generally been refuted in the last ten years, in this paper we show that the original 'Delayed Choice Quantum Eraser Experiment', 1st performed by Yoon-Ho Kim, R. Yu, S.P. Kulik, Y.H. Shih, designed by Marlan O. Scully & Druhl in 1982-1999, still features hidden topological properties that may have been overlooked by previous analysis, and which prohibit, by principle, the extraction of future-related or real-time information from the detection of the signal pa…
We investigate how quantum coincidence interferometry is affected by a controllable manipulation of transverse wave-vectors in type-II parametric down conversion using adaptive optics techniques. In particular, we discuss the possibility of spatial walk-off compensation in quantum interferometry and a new effect of even-order spatial aberration cancellation.
An intrinsically stable type-I optical parametric oscillator was built with a periodically poled KTiOPO4 (PPKTP) crystal to generate a stable bright, continuous-wave, broadband phase-squeezed beam. A 3.2 dB sensitivity enhancement of optical interferometry was demonstrated on weak electrooptic modulation signals within a 20 MHz squeezing bandwidth. This also realized a channel capacity increase beyond that of coherent optical communication.
We present a versatile, high-brightness, guided-wave source of polarization entangled photons, emitted at a telecom wavelength. Photon-pairs are generated using an integrated type-0 nonlinear waveguide, and subsequently prepared in a polarization entangled state via a stabilized fiber interferometer. We show that the single photon emission wavelength can be tuned over more than 50 nm, whereas the single photon spectral bandwidth can be chosen at will over more than five orders of magnitude (from 25 MHz to 4 THz). Moreover, by performing entanglement analysis, we demonstrate a high degree of co…
We investigate the connection between the shot-noise limit in linear interferometers and particle entanglement. In particular, we ask whether or not sub shot-noise sensitivity can be reached with all pure entangled input states of $N$ particles if they can be optimized with local operations. Results on the optimal local transformations allow us to show that for $N=2$ all pure entangled states can be made useful for sub shot-noise interferometry while for $N>2$ this is not the case. We completely classify the useful entangled states available in a bosonic two-mode interferometer. We apply our r…
The propagation of macroscopic entangled states over large distances in the presence of loss is of fundamental interest and may have practical applications as well. Here we describe two different techniques in which state discrimination can be used to violate Bell's inequality with macroscopic phase-entangled coherent states. We find that Bell's inequality can be violated by these macroscopic states over a distance of approximately 400 km in commercially-available optical fibers.
Sensing and measurement tasks in severely adverse conditions such as loss, noise and dephasing can be improved by illumination with quantum states of light. Previous results have shown a modest reduction in the number of measurements necessary to achieve a given precision. Here, we compare three illumination strategies for estimating the relative phase in a noisy, lossy interferometer. When including a common phase fluctuation in the noise processes, we show that using an entangled probe achieves an advantage in parameter estimation precision that scales with the number of entangled modes. Thi…
We have observed the stationary interference oscillations of a triple-entangled neutron state in an interferometric experiment. Time-dependent interaction with two radio-frequency (rf) fields enables coherent manipulation of an energy degree of freedom in a single neutron. The system is characterized by a multiply entangled state governed by a Jaynes-Cummings Hamiltonian. The experimental results confirm coherence of the manipulation as well as the validity of the description.
Optical interferometry has been a long-standing setup for characterization of quantum states of light. Both the linear and the nonlinear interferences can provide information about the light statistics an underlying detail of the light-matter interactions. Here we demonstrate how interferometric detection of nonlinear spectroscopic signals may be used to improve the measurement accuracy of matter susceptibilities. Light-matter interactions change the photon statistics of quantum light, which are encoded in the field correlation functions. Application is made to the Hong-Ou-Mandel two-photon in…
Differential interferometry (DI) with two coupled sensors is a most powerful approach for precision measurements in presence of strong phase noise. However DI has been studied and implemented only with classical resources. Here we generalize the theory of differential interferometry to the case of entangled probe states. We demonstrate that, for perfectly correlated interferometers and in the presence of arbitrary large phase noise, sub-shot noise sensitivities -- up to the Heisenberg limit -- are still possible with a special class of entangled states in the ideal lossless scenario. These sta…
We demonstrate optical interferometry beyond the limits imposed by the photon wavelength using 'triggered' entangled photon pairs from a semiconductor quantum dot. Interference fringes of the entangled biphoton state reveals a periodicity half of that obtained with the single photon, and much less than that of the pump laser. High fringe visibility indicates that biphoton interference is less sensitive to decoherence than interference of two sequential single photons. The results suggest that quantum interferometry may be possible using a semiconductor LED-like device.
We propose a Ramsey interferometry experiment using an entangled state of N atoms to reach the Heisenberg limit for the estimation of an atomic phase shift if the atom number parity is perfectly determined. In a more realistic situation, due to statistical fluctuations of the atom source and the finite detection efficiency, the parity is unknown. We then achieve about half the Heisenberg limit. The scheme involves an ensemble of circular Rydberg atoms which dispersively interact successively with two initially empty microwave cavities. The scheme does not require very high-Q cavities. An exper…
The archetypal quantum interferometry experiment yields an interference pattern that results from the indistinguishability of two spatiotemporal paths available to a photon or to a pair of entangled photons. A fundamental challenge in quantum interferometry is to perform such experiments with a higher number of paths, and over large distances. In particular, the distribution of such highly entangled states in long-haul optical fibers is one of the core concepts behind quantum information networks. We demonstrate that using indistinguishable frequency paths instead of spatiotemporal ones allows…
Entanglement between degrees of freedom, namely between the spin, path and (total) energy degrees of freedom, for single neutrons is exploited. We implemented a triply entangled Greenberger-Horne-Zeilinger(GHZ)-like state and coherently manipulated relative phases of two-level quantum subsystems. An inequality derived by Mermin was applied to analyze the generated GHZ-like state: we determined the four expectation values and finally obtained M=2.558 +/- 0.004 which is clearly above the threshold of 2. This demonstrates the violation of a Mermin-like inequality for triply entangled GHZ-like sta…
Quantum phenomena such as entanglement can improve fundamental limits on the sensitivity of a measurement probe. In optical interferometry, a probe consisting of $N$ entangled photons provides up to a $\sqrt{N}$ enhancement in phase sensitivity compared to a classical probe of the same energy. Here, we employ high-gain parametric down-conversion sources and photon-number-resolving detectors to perform interferometry with heralded quantum probes of sizes up to $N=8$ (i.e. measuring up to 16-photon coincidences). Our probes are created by injecting heralded photon-number states into an interfero…
Atomic (qubit) and optical or microwave (modal) phase-estimation protocols are placed on the same footing in terms of quantum-circuit diagrams. Circuit equivalences are used to demonstrate the equivalence of protocols that achieve the Heisenberg limit by employing entangled superpositions of Fock states, such as N00N states. The key equivalences are those that disentangle a circuit so that phase information is written exclusively on a mode or modes or on a qubit. The Fock-state-superposition phase-estimation circuits are converted to use entangled coherent-state superpositions; the resulting p…
The thesis is divided into three parts. In the first part a new theoretical analysis of interferometric experiments by Alley-Shih, Ou-Mandel and the entanglement swapping experiment is performed. It is shown that the double- and single-photon distinguishability is not necessary for the experiments to be genuine tests against local realism. In the second part, basing on simple geometrical properties of Hilbert space, new, stronger Bell inequalities for M qubits in a maximally entangled state are derived. Application of the same method to two maximally entangled qubits yields an inequality for a…
We show how the entangled photons produced in parametric down conversion can be used to improve the sensitivity of a Sagnac interferometer. Two-photon and four-photon coincidences increases the sensitivity by a factor of two and four respectively. Our results apply to sources with arbitrary pumping and squeezing parameters.
We propose an interferometry technique, by using electromagnetically induced transparency phenomena, for measuring classical force. The classical force is estimated by measuring the phase at the output of the interferometer. The proposed measurement mechanism satisfies quantum non-demolition measurement conditions leading to back-action evasion. We further derive the sufficient condition under which the thermal noise in the interferometer is negligible. With no back-action noise and no thermal noise, the sensitivity of this technique is limited by shot noise only.
Entanglement is not only fundamental for understanding multipartite quantum systems but also generally useful for quantum information applications. Despite much effort devoted so far, little is known about minimal resources for detecting entanglement and also comparisons to tomography which reveals the full characterization. Here, we show that all entangled states can in general be detected in an experimental scheme that estimates the fidelity of two pure quantum states. An experimental proposal is presented with a single Hong-Ou-Mandel interferometry in which only two detectors are applied re…
The Sagnac interferometry has been widely used to measure rotation frequency. Beyond the conventional single-particle Sagnac interferometry, we propose an atomic Sagnac interferometry via multi-particle entangled states. In our scheme, an ensemble of entangled two-state Bose atoms are moved in a ring by a state-dependent rotating potential and then are recombined for interference via Ramsey pulses after a specific time determined by the state-dependent rotating potential. The ultimate rotation sensitivity can be improved to the Heisenberg limit if the initial internal degrees of freedom are en…
We investigate an optimal distance of two components in an entangled coherent state for quantum phase estimation in lossy interferometry. The optimal distance is obtained by an economical point, representing the quantum Fisher information that we can extract per input energy. Maximizing the formula of the quantum Fisher information over an input mean photon number, we show that, as the losses of the interferometer increase, it can be more beneficial to prepare an initially entangled coherent state that is less entangled. This represents that the optimal distance of the two-mode components decr…
Gravitational time dilation in quantum clock interferometry with entangled multi-photon states and quantum memories
Humboldt-Universität zu Berlin（柏林洪堡大学）；ZARM, Unversität Bremen（不来梅大学ZARM中心）；Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien（维也纳量子科学与技术中心，原子物理研究所，维也纳工业大学）
We report on the the experimental realization of hyper-entangled two photon states, entangled in polarization and momentum. These states are produced by a high brilliance parametric source of entangled photon pairs with peculiar characteristics of flexibility in terms of state generation. The quality of the entanglement in the two degrees of freedom has been tested by multimode Hong-Ou-Mandel interferometry.
We present a new approach to engineering broadband sources of entangled photon pairs for quantum interferometry. The source is based on quasi-phase-matched spontaneous parametric down conversion in a titanium diffused periodically poled lithium niobate waveguide with a strongly-chirped poling period. The proposed non-standard asymmetric poling mitigates phase distortions associated with the process of chirping. Asymmetric poling significantly broadens the entangled source bandwidth while preserving high visibility quantum interferometric sensing.
Using a linear optical elements and post-selection, we construct an entangled polarization state of three photons in the same spatial mode. This state is analogous to a ``photon-number path entangled state'' and can be used for super-resolving interferometry. Measuring a birefringent phase shift, we demonstrate two- and three-fold improvements in phase resolution.
A method for performing nonlocal interferometry using phase-entangled macroscopic coherent states is described. The required entanglement can be generated using weak nonlinearities while Bell's inequality can be violated using single photons as a probe. The entanglement is relatively robust against photon loss and Bell's inequality can be violated over a relatively large distance in optical fibers despite the fact that a large number of photons are absorbed in the process.
We consider the problem of establishing entangled states of optimal singlet fraction and negativity between two remote parties for every use of a noisy quantum channel and trace-preserving LOCC under the assumption that the parties do not share prior correlations. We show that for a family of quantum channels in every finite dimension $d\geq3$, one-shot optimal singlet fraction and entanglement negativity are attained only with appropriate nonmaximally entangled states. We further show that the generalization of the formula that exactly computes one-shot optimal singlet fraction for qubit chan…
We demonstrate accurate phase measurement from low photon level interference data using a constrained optimization method that takes into account the expected redundancy in the unknown phase function. This approach is shown to have significant noise advantage over traditional methods such as balanced homodyning or phase shifting that treat individual pixels in the interference data as independent of each other. Our interference experiments comparing the optimization method with the traditional phase shifting method show that when the same photon resources are used, the optimization method prov…
We propose a scheme to achieve a Mach-Zehnder interferometry using a quantized Bose-Josephson junction with negative charging energy. The quantum adiabatic evolution through a dynamical bifurcation is used to accomplish the beam splitting and recombination. The negative charging energy ensures the existence of a path-entangled state which enhances the phase measurement precision to the Heisenberg limit. A feasible detection procedure is also presented. The scheme should be realizable with current technology.
The authors demonstrate a form of two-photon-counting interferometry by measuring the coincidence counts between single-photon-counting detectors at an output port of a Mach-Zehnder Interferometer (MZI) following injection of broad-band time-frequency-entangled photon pairs (EPP) generated from collinear spontaneous parametric down conversion into a single input port. Spectroscopy and refractometry are performed on a sample inserted in one internal path of the MZI by scanning the other path in length, which acquires phase and amplitude information about the samples linear response. Phase modul…
Most matter-wave interferometry (MWI) schemes for quantum sensing are so far evaluated in ideal situations without noises. In this work, we provide assessments of generic multiqubit MWI schemes under Markovian dephasing noises. We find that for certain classes of the MWI schemes with scale factors that are nonlinearly dependent on the interrogation time, the optimal precision of maximally entangled probes \emph{decreases} with increasing the particle number $N$, for both independent and collective dephasing situations. This result challenges the conventional wisdom found in dephasing Ramsey-ty…
Recent investigations suggest that the use of non-classical states of light, such as entangled photon pairs, may open new and exciting avenues in experimental two-photon absorption spectroscopy. Despite several experimental studies of entangled two-photon absorption (eTPA), there is still a heated debate on whether eTPA has truly been observed. This interesting debate has arisen, mainly because it has been recently argued that single-photon-loss mechanisms, such as scattering or hot-band absorption may mimic the expected entangled-photon linear absorption behavior. In this work, we focus on tr…
Analytic higher-order momentum correlation functions associated with the time-of-flight spectroscopy of three ultracold fermionic atoms singly-confined in a linear three-well optical trap are presented, corresponding to the W- and Greenberger-Horne-Zeilinger-type (GHZ) states that belong to characteristic classes of tripartite entanglement and represent the strong-interaction regime captured by a three-site Heisenberg Hamiltonian. The methodology introduced here contrasts with and goes beyond that based on the standard Wick's factorization scheme; it enables determination of both third-order a…
Ramsey interferometry allows the estimation of the phase $ϕ$ of rotation of the pseudospin vector of an ensemble of two-state quantum systems. For $ϕ$ small, the noise-to-signal ratio scales as the spin-squeezing parameter $ξ$, with $ξ<1$ possible for an entangled ensemble. However states with minimum $ξ$ are not optimal for single-shot measurements of an arbitrary phase. We define a phase-squeezing parameter, $ζ$, which is an appropriate figure-of-merit for this case. We show that (unlike the states that minimize $ξ$), the states that minimize $ζ$ can be created by evolving an unentangled sta…
We analyze phase interferometry realized with a bosonic Josephson junction made of trapped dilute and ultracold atoms. By using a suitable phase sensitivity indicator we study the zero temperature junction states useful to achieve sub shot-noise precisions. Sub shot-noise phase shift sensitivities can be reached even at finite temperature under a suitable choice of the junction state. We infer a scaling law in terms of the size system (that is, the number of particles) for the temperature at which the shot-noise limit is not overcome anymore
I analyze a metrological strategy for improving the precision of frequency estimation via Ramsey interferometry with strings of atoms in the presence of correlated dephasing. This strategy does not employ entangled states, but rather a product state which evolves into a stationary state under the influence of correlated dephasing. It is shown that by using this state an improvement in precision compared to standard Ramsey interferometry can be gained. This improvement is not an improvement in scaling, i.e. the estimation precision has the same scaling with the number of atoms as the standard q…
We study in detail a system of two interferometers aimed to the detection of extremely faint phase-fluctuations. This system can represent a breakthrough for detecting a faint correlated signal that would remain otherwise undetectable even using the most sensitive individual interferometric devices, that are limited by the shot noise. If the two interferometers experience identical phase-fluctuations, like the ones introduced by the so called "holographic noise", this signal should emerge if their output signals are correlated, while the fluctuations due to shot noise and other independent con…
We give a simple multiround strategy that permits to beat the shot noise limit when performing interferometric measurements even in the presence of loss. In terms of the average photon number employed, our procedure can achieve twice the sensitivity of conventional interferometric ones in the noiseless case. In addition, it is more precise than the (recently proposed) optimal two-mode strategy even in the presence of loss.
We analyze the ultimate bounds on the phase sensitivity of an interferometer, given the constraint that the state input to the interferometer's initial 50:50 beamsplitter $B$ is a product state of the two input modes. Requiring a product state is a natural restriction: if one were allowed to input an arbitrary, entangled two-mode state $|Ξ\rangle$ to the beamsplitter, one could generally just as easily input the state $B|Ξ\rangle$ directly into the two modes after the beamsplitter, thus rendering the beamsplitter unnecessary. We find optimal states for a fixed photon number and for a fixed mea…
