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 coupled to laser-probe field fluctuation. We present, for the first time, new developments for robust hyper Ramsey-Bordé and Mach-Zehnder interferometers, where we protect wavepacket interferences against distortion on frequency or phase measurement related to residual Doppler effects and light-shifts coupled to a pulse area error. Quantum matter-wave sensors with composite pulses and ultra-cold sources will offer detection of inertial effects inducing phase-shifts with better accuracy, to generate hyper-robust optical clocks and improving tests of fundamental physics, to realize a new class of atomic interferometers tracking space-time gravitational waves with a very high sensitivity.
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 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.
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 …
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 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…
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 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…
We present results on a free-space atom interferometer operating on the first order magnetically insensitive |F=1,mF=0> -> |F=2,mF=0> transition of Bose-condensed 87Rb atoms. A pulsed atom laser is output-coupled from a Bose-Einstein condensate and propagates through a sequence of two internal state beam splitters, realized via coherent Raman transitions between the two interfering states. We observe Ramsey fringes with a visibility close to 100% and determine the current and the potentially achievable interferometric phase sensitivity. This system is well suited to testing recent proposals fo…
We demonstrate Ramsey-Bordé (RB) atom interferometry for high performance laser stabilization with fractional frequency instability $<2 \times 10^{-16}$ for timescales between 10 and 1000s. The RB spectroscopy laser interrogates two counterpropagating $^{40}$Ca beams on the $^1$S$_0$ -- $^3$P$_1$ transition at 657 nm, yielding 1.6 kHz linewidth interference fringes. Fluorescence detection of the excited state population is performed on the (4s4p) $^3$P$_1$ -- (4p$^2$) $^3$P$_0$ transition at 431 nm. Minimal thermal shielding and no vibration isolation are used. These stability results surpass …
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）
We report a new experimental scheme which combines atom interferometry with Bloch oscillations to provide a new measurement of the ratio $h/m_{\mathrm{Rb}}$. By using Bloch oscillations, we impart to the atoms up to 1600 recoil momenta and thus we improve the accuracy on the recoil velocity measurement. The deduced value of $h/m_{\mathrm{Rb}}$ leads to a new determination of the fine structure constant $α^{-1}=137.035 999 45 (62)$ with a relative uncertainty of $4.6\times 10^{-9}$. The comparison of this result with the value deduced from the measurement of the electron anomaly provides the mo…
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…
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…
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 …
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.
We propose a set of experiments in which Ramsey-fringe techniques are tailored to probe transitions originating and terminating on the same ground state level. When pulses of resonant radiation, separated by a time delay $% T, $ interact with atoms, it is possible to produce Ramsey fringes having widths of order 1/T. If each pulse contains two counterpropagating travelling wave modes, the atomic wave function is split into two or more components having different center-of-mass momenta. Matter-wave interference of these components leads to atomic gratings, which have been observed in both spati…
A Ramsey-type interferometer is suggested, employing a cold trapped ion and two time-delayed off-resonant femtosecond laser pulses. The laser light couples to the molecular polarization anisotropy, inducing rotational wavepacket dynamics. An interferogram is obtained from the delay dependent populations of the final field-free rotational states. Current experimental capabilities for cooling and preparation of the initial state are found to yield an interferogram visibility of more than 80\%. The interferograms can be used to determine the polarizability anisotropy with an accuracy of about $\p…
We propose and demonstrate a new scheme for atom interferometry, using light pulses inside an optical cavity as matter wave beamsplitters. The cavity provides power enhancement, spatial filtering, and a precise beam geometry, enabling new techniques such as low power beamsplitters ($<100 \mathrm{μW}$), large momentum transfer beamsplitters with modest power, or new self-aligned interferometer geometries utilizing the transverse modes of the optical cavity. As a first demonstration, we obtain Ramsey-Raman fringes with $>75\%$ contrast and measure the acceleration due to gravity, $\mathit{g}$, t…
We theoretically discuss an implementation of a Sagnac interferometer with cold atoms. In contrast to currently existing schemes our protocol does not rely on any free propagation of atoms. Instead it is based on superpositions of fully confined atoms and state-dependent transport along a closed path. Using Ramsey sequences for an atomic clock, the accumulated Sagnac phase is encoded in the resulting population imbalance between two internal (clock) states. Using minimal models for the above protocol we analytically quantify limitations arising from atomic dynamics and finite temperature. We d…
High-precision magnetic field measurement is an ubiquitous issue in physics and a critical task in metrology. Generally, magnetic field has DC and AC components and it is hard to extract both DC and AC components simultaneously. The conventional Ramsey interferometry can easily measure DC magnetic fields, while it becomes invalid for AC magnetic fields since the accumulated phases may average to zero. Here, we propose a scheme for simultaneous measurement of DC and AC magnetic fields by combining Ramsey interferometry and rapid periodic pulses. In our scheme, the interrogation stage is divided…
In this paper we present a short overview of atom interferometry based on light pulses. We discuss different implementations and their applications for high precision measurements. We will focus on the determination of the ratio h/m of the Planck constant to an atomic mass. The measurement of this quantity is performed by combining Bloch oscillations of atoms in a moving optical lattice with a Ramsey-Bordé interferometer.
We use differential Ramsey interferometry of ultracold atoms to characterize the vector light shift (VLS) from a far-off resonance optical dipole trap at $λ= 1064\,\mathrm{nm}$. The VLS manifests as a `fictitious' magnetic field, which we perceive as a change in the Larmor frequency of two spinor condensates exposed to different intensities of elliptically polarized light. We use our measurement scheme to diagnose the light-induced magnetic field and suppress it to $2.1(8)\times10^{-4}$ of its maximum value, by making the trapping light linearly polarized with a quarter-wave plate in each beam…
We demonstrate a single-photon stored-light interferometer, where a photon is stored in a laser-cooled atomic ensemble in the form of a Rydberg polariton with a spatial extent of $10 \times1\times1μm^3$. The photon is subject to a Ramsey sequence, i.e. `split' into a superposition of two paths. After a delay of up to 450 ns, the two paths are recombined to give an output dependent on their relative phase. The superposition time of 450 ns is equivalent to a free-space propagation distance of 135 m. We show that the interferometer fringes are sensitive to external fields, and suggest that stored…
We present up to 24-photon Bragg diffraction as a beam splitter in light-pulse atom interferometers to achieve the largest splitting in momentum space so far. Relative to the 2-photon processes used in the most sensitive present interferometers, these large momentum transfer beam splitters increase the phase shift 12-fold for Mach-Zehnder (MZ-) and 144-fold for Ramsey-Borde (RB-) geometries. We achieve a high visibility of the interference fringes (up to 52% for MZ or 36% for RB) and long pulse separation times that are possible only in atomic fountain setups. As the atom's internal state is n…
We offer interferometry models for thermal ensembles with one-body losses and the phenomenological inclusion of perturbations covering most of the thermal atom experiments. A possible extension to the many-body case is briefly discussed. The Ramsey pulses are assumed to have variable durations and the detuning during the pulses is distinguished from the detuning during evolution. Consequently, the pulses are not restricted to resonant operation and give more flexibility to optimize the interferometer to particular experimental conditions. On this basis another model is devised in which the con…
We evaluate the performance and phase diffusion of trapped $^{87}$Rb atoms in an atom-chip sensor with Ramsey interferometry and Hahn's spin echo in the time and phase domains. We trace out how the phase uncertainty of interference fringes grows with time. The phase-domain spin echo enables us to attain many-second-long phase diffusion with a low-cost local oscillator that otherwise seems unrealistic to obtain with such an oscillator. In the Ramsey experiment we record interference fringes with contrast decaying in $12$ s, and with a frequency uncertainty of $80$ mHz corresponding to the depha…
Using optical Ramsey interferometry, we precisely measure the laser-induced AC-stark shift on the $S_{1/2}$ -- $D_{5/2}$ "quantum bit" transition near 729 nm in a single trapped $^{40}$Ca$^+$ ion. We cancel this shift using an additional laser field. This technique is of particular importance for the implementation of quantum information processing with cold trapped ions. As a simple application we measure the atomic phase evolution during a $n \times 2π$ rotation of the quantum bit.
In an atomic interferometer, the phase shift due to rotation is proportional to the area enclosed by the split components of the atom. However, this model is unclear for an atomic interferometer demonstrated recently by Shahriar et al., for which the atom simply passes through a single-zone optical beam, consisting of a pair of bichromatic counter-propagating beams. During the passage, the atomic wave packets in two distinct internal states couple to each other continuously. The two internal states trace out a complicated trajectory, guided by the optical beams, with the amplitude and spread o…
Bragg diffraction has been used in atom interferometers because it allows signal enhancement through multiphoton momentum transfer and suppression of systematics by not changing the internal state of atoms. Its multi-port nature, however, can lead to parasitic interferometers, allows for intensity-dependent phase shifts in the primary interferometers, and distorts the ellipses used for phase extraction. We study and suppress these unwanted effects. Specifically, phase extraction by ellipse fitting and the resulting systematic phase shifts are calculated by Monte Carlo simulations. Phase shifts…
Current attempts to test local position invariance (LPI) compare different clock transition rates with classically exchanged signals. We propose an experimental scheme for the quantum test of LPI: an internal atomic clock interferometer comprising two interfering clocks within one atom. We prepare the atom in a superposition of two clock states and one ground state, which evolves coherently along two quantum clock oscillations into stable internal Ramsey interference patterns. The interference pattern with the shared ground state shows a visibility modulation, which can be interpreted as the b…
Non-local mass superpositions and optical clock interferometry in atomic ensemble quantum networks
University of Innsbruck（因斯布鲁克大学）；Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences（奥地利科学院量子光学和量子信息研究所）；Leibniz Universität Hannover（汉诺威莱布尼茨大学）；JILA, NIST and Department of Physics, University of Colorado（科罗拉多大学JILA、美国国家标准与技术研究院及物理系）；Center for Theory of Quantum Matter, University of Colorado（科罗拉多大学量子物质理论中心）
Ultracold atoms in optical lattices are a powerful tool for quantum simulation, precise measurement, and quantum computation. A fundamental problem in applying this quantum system is how to manipulate the higher bands or orbitals in Bloch states effectively. Here we mainly review our methods for manipulating high orbital ultracold atoms in optical lattices with different configurations. Based on these methods, we construct the atom-orbital qubit under nonadiabatic holonomic quantum control and Ramsey interferometry with trapped motional quantum states. Then we review the observation of the nov…
We perform Ramsey interferometry on an ultracold 87Rb ensemble confined in an optical dipoletrap. We use a π-pulse set at the middle of the interferometer to restore the coherence of the spinensemble by canceling out phase inhomogeneities and creating a spin echo in the contrast. However,for high atomic densities, we observe the opposite behavior: the π-pulse accelerates the dephasingof the spin ensemble leading to a faster contrast decay of the interferometer. We understand thisphenomenon as a competition between the spin-echo technique and an exchange-interaction drivenspin self-rephasing me…
