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 errors, the expectation value of the parity operator $Π$ has the general form, $\overline{\langle Π\rangle} = Π_0 \cos( N ϕ)$, where $ϕ$ is the interferometer phase and $N$ is the number of atoms prepared in the maximally entangled Greenberger--Horne--Zeilinger state. Correspondingly, the minimum phase uncertainty has the general form, $Δϕ= (Π_0 N)^{-1}$. Each error manifests itself through a reduction of the amplitude of the parity oscillations, $Π_0$, below the ideal value of $Π_0 = 1$. For each of the errors, we derive an analytic result that expresses the dependence of $Π_0$ on error parameter(s) and $N$, and also obtain a simplified approximate expression valid when the error is small. Based on the performed analysis, entanglement-enhanced atom interferometry appears to be feasible with existing experimental capabilities.
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…
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.
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…
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.
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…
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…
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.
In this paper, we present a brief overview of atom interferometry. This field of research has developed very rapidly since 1991. Atom and light wave interferometers present some similarities but there are very important differences in the tools used to manipulate these two types of waves. Moreover, the sensitivity of atomic waves and light waves to their environment is very different. Atom interferometry has already been used for a large variety of studies: measurements of atomic properties and of inertial effects (accelerations and rotations), new access to some fundamental constants, observa…
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…
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）
Chirped-pulse interferometry is a new interferometric technique encapsulating the advantages of the quantum Hong-Ou-Mandel interferometer without the drawbacks of using entangled photons. Both interferometers can exhibit even-order dispersion cancellation which allows high resolution optical delay measurements even in thick optical samples. In the present work, we show that finite frequency correlations in chirped-pulse interferometry and Hong-Ou-Mandel interferometry limit the degree of dispersion cancellation. Our results are important considerations in designing practical devices based on t…
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.
We illustrate how geometric gauge forces and topological phase effects emerge in quantum systems without employing assumptions that rely on adiabaticity. We show how geometric magnetism may be harnessed to engineer novel quantum devices including a velocity sieve, a component in mass spectrometers, for neutral atoms or neutrons. We outline a possible experimental setup that demonstrates topological interferometry for neutral spin 1/2 systems.
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.
It is a commonly stated that the acceleration sensitivity of an atom interferometer is proportional to the space-time area enclosed between the two interfering arms. Here we derive the interferometric phase shift for an extensive class of interferometers, and explore the circumstances in which only the inertial terms contribute. We then analyse various configurations in light of this geometric interpretation of the interferometric phase shift.
We have built an atom interferometer and, by applying an electric field on one of the two interfering beams, we have measured the static electric polarizability of lithium with a 0.66 % uncertainty. Our experiment is similar to an experiment done on sodium in 1995 by D. Pritchard and co-workers, with several improvements: the electric field can be calculated analytically and our phase measurements are very accurate. This experiment illustrates the extreme sensitivity of atom interferometry: when the atom enters the electric field, its velocity increases and the fractional change, equal to 4 x …
We study the preparation and manipulation of states involving a small number of interacting particles. By controlling the splitting and fusing of potential wells, we show how to interconvert Mott-insulator-like and trapped BEC-like states. We also discuss the generation of "Schrödinger cat" states by splitting a microtrap and taking into practical consideration the asymmetry between the resulting wells. These schemes can be used to perform multiparticle interferometry with neutral atoms, where interference effects can be observed only when all the participating particles are measured.
A method for mitigating the readout delay characteristic of Bragg-based atom interferometry is presented, utilizing an asymmetric Mach-Zehnder interferometer sequence to generate spatial fringes that are read out while still overlapped. The time of flight after the final beamsplitter is engineered to facilitate constructive overlap of the fringes on the output states. A noise analysis performed using a precision atom interferometer is presented, comparing the traditional separated symmetric scheme with that of the separated and overlapped asymmetric scheme showing no significant increase in sh…
We report on a novel experiment to generate non-classical atomic states via quantum non-demolition (QND) measurements on cold atomic samples prepared in a high finesse ring cavity. The heterodyne technique developed for the QND detection exhibits an optical shot-noise limited behavior for local oscillator optical power of a few hundred \muW, and a detection bandwidth of several GHz. This detection tool is used in single pass to follow non destructively the internal state evolution of an atomic sample when subjected to Rabi oscillations or a spin-echo interferometric sequence.
We propose a novel scheme for the lithography of arbitrary, two-dimensional nanostructures via matter-wave interference. The required quantum control is provided by a pi/2-pi-pi/2 atom interferometer with an integrated atom lens system. The lens system is developed such that it allows simultaneous control over atomic wave-packet spatial extent, trajectory, and phase signature. We demonstrate arbitrary pattern formations with two-dimensional 87Rb wavepackets through numerical simulations of the scheme in a practical parameter space. Prospects for experimental realizations of the lithography sch…
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…
A new technique for maintaining high contrast in an atom interferometer is used to measure large de Broglie wave phase shifts. Dependence of an interaction induced phase on the atoms' velocity is compensated by applying an engineered \emph{counter phase}. The counter phase is equivalent to a rotation and precisely determined by a frequency, and can be used to measure phase shifts due to interactions of unknown strength. Phase shifts of 150 radians (5 times larger than previously possible) have now been measured in an atom beam interferometer and we suggest that this technique can enable compar…
Quantum non-locality based on the well-known Bell inequality is of kinematic nature. A different type of quantum non-locality, the non-locality of the quantum equation of motion, is recently put forward with connection to the Aharonov-Bohm effect [Nature Phys. 6, 151 (2010)]. Evolution of the displacement operator provides an example to manifest such dynamic quantum non-locality. We propose an experiment using single-atom interferometry to test such dynamic quantum non-locality. We show how to measure evolution of the displacement operator with clod atoms in a spin-dependent optical lattice po…
Atom matterwave interferometry requires mirror and beamsplitter pulses that are robust to inhomogeneities in field intensity, magnetic environment, atom velocity and Zeeman sub-state. Pulse shapes determined using quantum control methods offer significantly improved interferometer performance by allowing broader atom distributions, larger interferometer areas and higher contrast. We have applied gradient ascent pulse engineering (GRAPE) to optimise the design of phase-modulated mirror pulses for a Mach-Zehnder light-pulse atom interferometer, with the aim of increasing fringe contrast when ave…
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…
Bragg diffraction is comparable to a hard-wall reflection if the Bragg condition is exactly fulfilled. However, in a neutron interferometer in the gravitational field (COW experiment) this is not the case and the momentum transfers should not be described by hard wall reflection, as it has been done in the commented article. Instead, and quite similar to the atom case, each mirror or beam splitter creates a constant momentum transfer given by the reciprocal lattice vector of the Bragg crystal. To lowest order there are no differences between the atom and the neutron case.
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 apply the new constraints from atom-interferometry searches for screening mechanisms to the symmetron model, finding that these experiments exclude a previously unexplored region of parameter space. We discuss the possibility of networks of domain walls forming in the vacuum chamber, and how this could be used to discriminate between models of screening.
We provide an introduction into the field of atom optics and review our work on interferometry with cold atoms, and in particular with Bose-Einstein condensates. Here we emphasize applications of atom interferometry with sources of this kind. We discuss tests of the equivalence principle, a quantum tiltmeter, and a gravimeter.
We develop an operator-based description of two types of multimode-entangled single-neutron quantum optical devices: Wollaston prisms and radio-frequency spin flippers in inclined magnetic field gradients. This treatment is similar to the approach used in quantum optics, and is convenient for the analysis of quantum contextuality measurements in certain types of neutron interferometers. We describe operationally the way multimode-entangled single-neutron states evolve in these devices, and provide expressions for the associated operators describing the dynamics, in the limit in which the neutr…
We theoretically investigate the use of quantum non-demolition measurement to enhance the sensitivity of atom interferometry with Bose-condensed atoms. In particular, we are concerned with enhancing existing high-precision atom interferometry apparatuses, so restrict ourselves to dilute atomic samples, and the use of free-propagating light, or optical cavities in the weak-coupling regime. We find the optimum parameter regime that balances between spin squeezing and atomic loss, and find that significant improvements in sensitivity are possible. Finally, we consider the use of squeezed light, a…
