We show that the statistical properties of a Coulomb crystal can be measured by means of a standard interferometric procedure performed on the spin of one ion in the chain. The ion spin, constituted by two internal levels of the ion, couples to the crystal modes via spatial displacement induced by photon absorption. The loss of contrast in the interferometric signal allows one to measure the autocorrelation function of the crystal observables. Close to the critical point, where the chain undergoes a second-order phase transition to a zigzag structure, the signal gives the behaviour of the correlation function at the critical point.
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…
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 propose a generalization of the Tonks-Girardeau model that describes a coherent gas of cold two-level Bosons which interact with two external fields in a Ramsey interferometer. They also interact among themselves by contact collisions with interchange of momentum and internal state. We study the corresponding Ramsey fringes and the quantum projection noise which, essentially unaffected by the interactions, remains that for ideal Bosons. The dual system of this gas, an ideal gas of two-level Fermions coupled by the interaction with the separated fields, produces the same fringes and noise fl…
We perform atom interferometry using the Zeeman sublevels of a spin-2 Bose-Einstein condensate of $^{87}$Rb. The observed fringes are strongly peaked, and fringe repetition rates higher than the fundamental Ramsey frequency are found in agreement with a simple theory based on spin rotations. With a suitable choice of initial states, the interferometer could function as a useful tool for magnetometry and studies of spinor dynamics in general.
We report a narrowing of the interference pattern obtained in an atomic Ramsey interferometer if the two separated fields have different frequency and their phase difference is controlled. The width of the Ramsey fringes depends inversely on the free flight time of ground state atoms before entering the first field region in addition to the time between the fields. The effect is stable also for atomic wavepackets with initial position and momentum distributions and for realistic mode functions.
We study the non-relativistic limit of a paradigmatic model in Relativistic Quantum Mechanics, the two-dimensional Dirac oscillator. Remarkably, we find a novel kind of Zitterbewegung which persists in this non-relativistic regime, and leads to an observable deformation of the particle orbit. This effect can be interpreted in terms of a Ramsey Interferometric phenomenon, allowing an insightful connection between Relativistic Quantum Mechanics and Quantum Optics. Furthermore, subsequent corrections to the non-relativistic limit, which account for the usual spin-orbit Zitterbewegung, can be neat…
We adopt the Ramsey's method of separated oscillatory fields to study coherences of the mechanical system in an optomechanical resonator. The high resolution Ramsey fringes are observed in the emission optical field, when two pulses separated in time are applied. We develop a theory to describe the transient optomechanical behavior underlying the Ramsey fringes. We also perform the experimental demonstration using a silica microresonator. The method is versatile and can be adopted to different types of mechanical resonators, electromechanical resonators.
We theoretically investigate the dynamics of a gas of strongly interacting Rydberg atoms subject to a time-domain Ramsey interferometry protocol. The many-body dynamics is governed by an Ising-type Hamiltonian with long range interactions of tunable strength. We analyze and model the contrast degradation and phase accumulation of the Ramsey signal and identify scaling laws for varying interrogation times, ensemble densities, and ensemble dimensionalities.
We quantify the impact of spatio-temporally correlated Gaussian quantum noise on frequency estimation by Ramsey interferometry. While correlations in a classical noise environment can be exploited to reduce uncertainty relative to the uncorrelated case, we show that quantum noise environments with frequency asymmetric spectra generally introduce additional sources of uncertainty due to uncontrolled entanglement of the sensing system mediated by the bath. For the representative case of collective noise from bosonic sources, and experimentally relevant collective spin observables, we find that t…
Realizing highly sensitive interferometry is essential to accurate observation of quantum properties. Here we study two kinds of Ramsey interference fringes in a whispering-gallery resonator, where the coherent phonons for free evolution can be achieved by stimulated Brillouin scattering. These two different fringes appear, respectively, in the regimes of rotating wave approximation (RWA) and anti-RWA. Our work shows particularly that the anti-RWA Ramsey interference takes some quantum properties of squeezing, which enhances the strength and visibility of the fringes and shows robustness again…
Ramsey interferometers have wide applications in science and engineering. Compared with the traditional interferometer based on internal states, the interferometer with external quantum states has advantages in some applications for quantum simulation and precision measurement. Here, we develop a Ramsey interferometry with Bloch states in S- and D-band of a triangular optical lattice for the first time. The key to realizing this interferometer in two-dimensionally coupled lattice is that we use the shortcut method to construct $π/2$ pulse. We observe clear Ramsey fringes and analyze the decohe…
We study the time-dependent dynamical phase of fractional quasiparticles in quantum Hall states using Ramsey interferometry. A Ramsey two-pulse voltage modulation generates an interference term in the current noise of a quantum point contact oscillating with the dynamical phase. We show that the interference pattern probes the Green's function of the fractional quasi-particles in the time domain and reveals the fractional charge. We address both the case of a point-like tunnel junction and the case of momentum-resolved tunneling which also provides information on the speed of those quasipartic…
We adapt a typical Ramsey interferometer by inserting a linear accelerator capable of accelerating an atom inside a single-mode cavity. We demonstrate that this simple scheme allows us to estimate the effects of acceleration radiation via interferometric visibility. By using a Rydberg-like atom, our results suggest that, for the transition regime of the order of GHz and interaction time of 1 ns, acceleration radiation effects can be observable for accelerations as low as $10^{17}$ m/s$^2$.
We examine the passage of ultracold two-level atoms through two separated laser fields for the nonresonant case. We show that implications of the atomic quantized motion change dramatically the behavior of the interference fringes compared to the semiclassical description of this optical Ramsey interferometer. Using two-channel recurrence relations we are able to express the double-laser scattering amplitudes by means of the single-laser ones and to give explicit analytical results. When considering slower and slower atoms, the transmission probability of the system changes considerably from a…
Estimating multiple parameters simultaneously is of great importance to measurement science and application. For a single parameter, atomic Ramsey interferometry (or equivalently optical Mach-Zehnder interferometry) is capable of providing the precision at the standard quantum limit (SQL) using unentangled probe states as input. In such an interferometer, the first beam splitter represented by unitary transformation $U$ generates a quantum phase sensing superposition state, while the second beam splitter $U^{-1}$ recombines the phase encoded paths to realize interferometric sensing in terms of…
We discuss quantum variational optimization of Ramsey interferometry with ensembles of $N$ entangled atoms, and its application to atomic clocks based on a Bayesian approach to phase estimation. We identify best input states and generalized measurements within a variational approximation for the corresponding entangling and decoding quantum circuits. These circuits are built from basic quantum operations available for the particular sensor platform, such as one-axis twisting, or finite range interactions. Optimization is defined relative to a cost function, which in the present study is the Ba…
We introduce a Ramsey pulse scheme which extracts the non-Hermitian Hamiltonian associated to an arbitrary Lindblad dynamics. We propose a realted protocol to measure via interferometry a generalised Loschmidt echo of a generic state evolving in time with the non-Hermitian Hamiltonian itself, and we apply the scheme to a one-dimensional weakly interacting Bose gas coupled to a stochastic atomic impurity. The Loschmidt echo is mapped into a functional integral from which we calculate the long-time decohering dynamics at arbitrary impurity strengths. For strong dissipation we uncover the phenome…
Ramsey interferometers (RIs) using internal electronic or nuclear states find wide applications in science and engineering. We develop a matter wave Ramsey interferometer for motional quantum states exploiting the S- and D-bands of an optical lattice and identify the different de-phasing and de-coherence mechanisms. We implement a band echo technique, employing repeated $π$-pulses. This suppresses the de-phasing evolution and significantly increase the coherence time of the motional state interferometer by one order of magnitude. We identify thermal fluctuations as the main mechanism for the r…
We discuss the frequency and visibility of atom-molecule Ramsey fringes observed in recent experiments by Claussen et al.[Phys. Rev. A 67, 060701 (2003)]. In these experiments a 85Rb Bose-Einstein condensate was exposed to a sequence of magnetic field pulses on the high field side of the 155 G Feshbach resonance. The observed oscillation frequencies largely agree with the theoretically predicted magnetic field dependence of the binding energy of the highest excited diatomic vibrational state, except for a small region very close to the singularity of the scattering length. Our analytic treatme…
We minimize the stray electric field in a linear Paul trap quickly and accurately, by applying interferometry pulse sequences to a trapped ion optical qubit. The interferometry sequences are sensitive to the change of ion equilibrium position when the trap stiffness is changed, and we use this to determine the stray electric field. The simplest pulse sequence is a two-pulse Ramsey sequence, and longer sequences with multiple pulses offer a higher precision. The methods allow the stray field strength to be minimized beyond state-of-the-art levels, with only modest experimental requirements. Usi…
Every measurement of the population in an uncorrelated ensemble of two-level systems is limited by what is known as the quantum projection noise limit. Here, we present quantum projection noise limited performance of a Ramsey type interferometer using freely propagating coherent atoms. The experimental setup is based on an electro-optic modulator in an inherently stable Sagnac interferometer, optically coupling the two interfering atomic states via a two-photon Raman transition. Going beyond the quantum projection noise limit requires the use of reduced quantum uncertainty (squeezed) states. T…
We propose to use Ramsey interferometry and single-site addressability, available in synthetic matter such as cold atoms or trapped ions, to measure real-space and time resolved spin correlation functions. These correlation functions directly probe the excitations of the system, which makes it possible to characterize the underlying many-body states. Moreover they contain valuable information about phase transitions where they exhibit scale invariance. We also discuss experimental imperfections and show that a spin-echo protocol can be used to cancel slow fluctuations in the magnetic field. We…
We study ensembles of Rydberg atoms in a confined electromagnetic environment such as provided by a microwave cavity. The competition between standard free space Ising type and cavity-mediated interactions leads to the emergence of different regimes where the particle-particle couplings range from the typical van der Waals $r^{-6}$ behavior to $r^{-3}$ and to $r$-independence. We apply a Ramsey spectroscopic technique to map the two-body interactions into a characteristic signal such as intensity and contrast decay curves. As opposed to previous treatments requiring high-densities for consider…
We consider a large class of Ramsey interferometry protocols which are enhanced by squeezing and un-squeezing operations before and after a phase signal is imprinted on the collective spin of $N$ particles. We report an analytical optimization for any given particle number and strengths of (un-)squeezing. These results can be applied even when experimentally relevant decoherence processes during the squeezing and un-squeezing interactions are included. Noise between the two interactions is however not considered in this work. This provides a generalized characterization of squeezing echo proto…
Temporal modes (TM) are a new basis for storage and retrieval of quantum information in states of light. The full TM manipulation toolkit requires a practical quantum pulse gate (QPG), which is a device that unitarily maps any given TM component of the optical input field onto a different, easily separable subspace or degree of freedom. An ideal QPG must "separate" the selected TM component with unit efficiency, whilst avoiding crosstalk from orthogonal TMs. All attempts at implementing QPGs in pulsed-pump traveling-wave systems have been unable to satisfy both conditions simultaneously. This …
A new generation of atomic sensors using ultra-narrow optical clock transitions and composite pulses are pushing quantum engineering control to a very high level of precision for applied and fundamental physics. Here, we propose a new version of Ramsey-Bordé interferometry introducing arbitrary composite laser pulses with tailored pulse duration, Rabi field, detuning and phase-steps. We explore quantum metrology below the $10^{-18}$ level of fractional accuracy by a fine tuning control of light excitation parameters protecting ultra-narrow optical clock transitions against residual light-shift…
We have realized a magnetic tensor gradiometer by interferometrically measuring the relative phase between two spatially separated Bose-Einstein condensates (BECs). We perform simultaneous Ramsey interferometry of the proximate $^{87}$Rb spin-1 condensates in freefall and infer their relative Larmor phase -- and thus the differential magnetic field strength -- with a common-mode phase noise suppression exceeding $50\,\mathrm{dB}$. By appropriately biasing the magnetic field and separating the BECs along orthogonal directions, we measure the magnetic field gradient tensor of ambient and applied…
A new class of atomic interferences using ultra-narrow optical transitions are pushing quantum engineering control to a very high level of precision for a next generation of sensors and quantum gate operations. In such context, we propose a new quantum engineering approach to Ramsey-Bordé interferometry introducing multiple composite laser pulses with tailored pulse duration, Rabi field amplitude, frequency detuning and laser phase-step. We explore quantum metrology with hyper-Ramsey and hyper-Hahn-Ramsey clocks below the $10^-18$ level of fractional accuracy by a fine tuning control of light …
We propose an interferometric scheme based on an untrapped nano-object subjected to gravity. The motion of the center of mass (c.m.) of the free object is coupled to its internal spin system magnetically, and a free flight scheme is developed based on coherent spin control. The wavepacket of the test object, under a spin-dependent force, may then be delocalized to a macroscopic scale. A gravity induced dynamical phase (accrued solely on the spin state, and measured through a Ramsey scheme) is used to reveal the above spatially delocalised superposition of the spin-nano-object composite system …
Exponential enhancement of sensitivity in Ramsey interferometry with optically thick ensemble of atoms
Kazan Quantum Center, Kazan National Research Technical University n.a. A.N. Tupolev-KAI（喀山量子中心，喀山国立研究技术大学（A.N. 图波列夫-CAI））；Department of Physics, McGill University（麦吉尔大学物理系）
The laser-like coherent emission at 391nm from N$_2$ gas irradiated by strong 800nm pump laser and weak 400nm seed laser is theoretically investigated. Recent experimental observations are well simulated, including temporal profile, optical gain and periodic modulation of the 391nm signal from N$_2^+$. Our calculation sheds light on the long standing controversy on whether population inversion is indispensable for the optical gain. We demonstrate the Ramsey interference fringes of the emission intensity at 391nm formed by additionally injecting another 800nm pump or 400nm seed, which are well …
Heisenberg-limited measurement protocols can be used to gain an increase in measurement precision over classical protocols. Such measurements can be implemented using, e.g., optical Mach-Zehnder interferometers and Ramsey spectroscopes. We address the formal equivalence between the Mach-Zehnder interferometer, the Ramsey spectroscope, and the discrete Fourier transform. Based on this equivalence we introduce the ``quantum Rosetta stone'', and we describe a projective-measurement scheme for generating the desired correlations between the interferometric input states in order to achieve Heisenbe…
Ramsey spectroscopy via coherent population trapping (CPT) is essential in precision measurements. The conventional CPT-Ramsey fringes contain numbers of almost identical oscillations and so that it is difficult to identify the central fringe. Here, we experimentally demonstrate a temporal spinwave Fabry-Pérot interferometry via double-$Λ$ CPT of laser-cooled $^{87}$Rb atoms. Due to the constructive interference of temporal spinwaves, the transmission spectrum appears as a comb of equidistant peaks in frequency domain and thus the central Ramsey fringe can be easily identified. From the optica…
Robust Diamond Quantum Sensing in Double-Quantum 4-Ramsey Interferometry by Dual-Feedback Scheme
Institute of Science Tokyo（科学技术研究所）；National Institute for Materials Science（国立材料研究所）；University of Tsukuba（筑波大学）；National Institutes for Quantum Science and Technology : QST（量子科学技术研究开发机构）；Tohoku University（东北大学）
Spectator-transition crosstalk in a spin-3/2 silicon-vacancy qudit in silicon carbide revealed by broadband Ramsey interferometry
Gwangju Institute of Science and Technology（光州科学技术院）；Linköping University（林雪平大学）；National Institutes for Quantum Science and Technology (QST)（国立量子科学和技术研究院）；Tohoku University（东北大学）；Korea Multi-purpose Accelerator Complex, Korea Atomic Energy Research Institute（韩国多功能加速器装置，韩国原子能研究所）
Out-of-equilibrium statistical mechanics is attracting considerable interest due to the recent advances in the control and manipulations of systems at the quantum level. Recently, an interferometric scheme for the detection of the characteristic function of the work distribution following a time-dependent process has been proposed [L. Mazzola {\it et al}, Phys. Rev. Lett. {\bf 110} 230602 (2013)]. There, it was demonstrated that the work statistics of a quantum system undergoing a process can be reconstructed by effectively mapping the characteristic function of work on the state of an ancilla…
We show how the interference between spatially separated states of the center of mass (COM) of a mesoscopic harmonic oscillator can be evidenced by coupling it to a spin and performing solely spin manipulations and measurements (Ramsey Interferometry). We propose to use an optically levitated diamond bead containing an NV center spin. The nano-scale size of the bead makes the motional decoherence due to levitation negligible. The form of the spin-motion coupling ensures that the scheme works for thermal states so that moderate feedback cooling suffices. No separate control or observation of th…
We report on a demonstration of Ramsey interferometry by three-dimensional motion with a trapped $^{171}Yb^+$ ion. We applied a momentum kick to the ion in a direction diagonal to the trap axes to initiate three-dimensional motion using a mode-locked pulse laser. The interference signal was analyzed theoretically to demonstrate three-dimensional matter-wave interference. This work paves the way to realizing matter-wave interferometry using trapped ions.
A longstanding goal of Akira Tonomura was to observe Hanbury Brown--Twiss anti-correlations between electrons in a field-emission free electron beam. The experimental results were reported in his 2011 paper with Tetsuji Kodama and Nobuyuki Osakabe [Phys. Rev. A 83, 063616 (2011)]. An open issue in such a measurement is whether the observed anti-correlations arise from quantum statistics, or are simply produced by Coulomb repulsion between electrons. In this paper we describe a simple classical model of Coulomb effects to estimate their effects in electron beam interferometry experiments, and c…
We investigate the back-flow of information in a system with a second-order structural phase transition, namely a quasi one-dimensional Coulomb crystal. Using standard Ramsey interferometry which couples a target ion (the system) to the rest of the chain (a phononic environment), we study the non-Markovian character of the resulting open system dynamics. We study two different time-scales and show that the back-flow of information pinpoints both the phase transition and different dynamical features of the chain as it approaches criticality. We also establish an exact link between the back-flow…
Ramsey interferometry provides a natural way to determine the coherence time of most qubit systems. Recent experiments on quantum dots however, demonstrated that dynamical nuclear spin polarization can strongly influence the measurement process, making it difficult to extract the $T_2^*$ coherence time using optical Ramsey pulses. Here, we demonstrate an alternative method for spin coherence measurement that is based on first-order coherence of photons generated in spin-flip Raman scattering. We show that if a quantum emitter is driven by a weak monochromatic laser, Raman coherence is determin…
We demonstrate a two-pulse Ramsey-type interferometer for non-classical motional states of a Bose-Einstein condensate in an anharmonic trap. The control pulses used to manipulate the condensate wavefunction are obtained from Optimal Control Theory and directly optimised to maximise the interferometric contrast. They permit a fast manipulation of the atomic ensemble compared to the intrinsic decay and many-body dephasing effects, and thus to reach an interferometric contrast of 92% in the experimental implementation.
Quantum phase estimation is a paradigmatic problem in quantum sensing andmetrology. Here we show that adaptive methods based on classical machinelearning algorithms can be used to enhance the precision of quantum phase estimation when noisy non-entangled qubits are used as sensors. We employ the Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms to this task and we identify the optimal feedback policies which minimize the Holevo variance. We benchmark these schemes with respect to scenarios that include Gaussian and Random Telegraph fluctuations as well as reduced Ram…
