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 phenomenology of a quantum many-body Zeno effect: corrections to the decoherence exponent resulting from the impurity self-energy becomes purely imaginary, in contrast to the regime of small dissipation where they instead enhance the decay of quantum coherences. Our results illustrate the prospects for experiments employing Ramsey interferometry to study dissipative quantum impurities in condensed matter and cold atoms systems.
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 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.
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 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 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…
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 fastest possible collective response of a quantum many-body system is related to its excitations at the highest possible energy. In condensed-matter systems, the corresponding timescale is typically set by the Fermi energy. Taking advantage of fast and precise control of interactions between ultracold atoms, we report on the observation of ultrafast dynamics of impurities coupled to an atomic Fermi sea. Our interferometric measurements track the non-perturbative quantum evolution of a fermionic many-body system, revealing in real time the formation dynamics of quasiparticles and the quantu…
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.
This article is based on the talk with the same title at the Blaubeuren meeting. First we discuss briefly the importance of time and time keeping, explaining the basic functioning of clocks in general and atomic clocks in particular, which rely on Ramsey interferometry. The usefulness of cold atoms is discussed as well as their limits in Bose-Einstein condensates. An alternative that we study is a different cold-atom regime: the Tonks-Girardeau (TG) gas of tightly confined and strongly interacting bosons. The TG gas is reviewed and then generalized for two-level atoms. Finally, we explore the …
Mapping the potential landscape with high spatial resolution is crucial for quantum technologies based on ultracold atoms. Yet, imaging optical dipole traps is challenging because purely optical methods, commonly used to profile laser beams in free space, are not applicable in vacuum. In this work, we demonstrate precise in-situ imaging of optical dipole traps by probing a hyperfine transition with Ramsey interferometry. Thereby, we obtain an absolute map of the potential landscape with micrometer resolution and shot-noise-limited spectral precision. The idea of the technique is to control the…
We introduce a primary thermometer which measures the temperature of a Bose-Einstein Condensate in the sub-nK regime. We show, using quantum Fisher information, that the precision of our technique improves the state-of-the-art in thermometry in the sub-nK regime. The temperature of the condensate is mapped onto the quantum phase of an atomic dot that interacts with the system for short times. We show that the highest precision is achieved when the phase is dynamical rather than geometric and when it is detected through Ramsey interferometry. Standard techniques to determine the temperature of …
We report Ramsey spectroscopy on the clock states of individual Cs impurities immersed in an ultracold Rb bath. We record both the interaction-driven phase evolution and the decay of fringe contrast of the Ramsey interference signal to obtain information about bath density or temperature nondestructively. The Ramsey fringe is modified by a differential shift of the collisional energy when the two Cs states superposed interact with the Rb bath. This differential shift is directly affected by the mean gas density and the details of the Rb-Cs interspecies scattering length, affecting the phase ev…
The challenge of understanding the dynamics of a mobile impurity in an interacting quantum many-body medium comes from the necessity of including entanglement between the impurity and excited states of the environment in a wide range of energy scales. In this paper, we investigate the motion of a finite mass impurity injected into a three-dimensional quantum Bose fluid as it starts shedding Bogoliubov excitations. We uncover a transition in the dynamics as the impurity's velocity crosses a critical value which depends on the strength of the interaction between the impurity and bosons as well a…
Recent work proposed a variant on Ramsey interferometry for coupled spin-$1/2$ systems that directly measures the retarded spin-spin Green's function. We expand on that work by investigating nonequilibrium retarded spin-spin Green's functions within the transverse-field Ising model. We derive the lowest four spectral moments to understand the short-time behavior and we employ a Lehmann-like representation to determine the spectral behavior. We simulate a Ramsey protocol for a nonequilibrium quantum spin system that consists of a coherent superposition of the ground state and diabatically excit…
Topological quantum phases cannot be characterized by Ginzburg-Landau type order parameters, and are instead described by non-local topological invariants. Experimental platforms capable of realizing such exotic states now include "synthetic" many-body systems such as ultracold atoms or photons. Unique tools available in these systems enable a new characterization of strongly correlated many-body states. Here we propose a general scheme for detecting topological order using interferometric measurements of elementary excitations. The key ingredient is the use of mobile impurities which bind to …
We investigate the system of a heavy impurity immersed in a degenerated Fermi gas, where the impurity's internal degree of freedom (pseudospin) is manipulated by a series of radiofrequency (RF) pulses at several different times. Applying the functional determinant approach, we carry out an essentially exact calculation of the Ramsey-interference-type responses to the RF pulses. These responses are universal functions of the multiple time intervals between the pulses for all time and can be regarded as multidimensional (MD) spectroscopy of the system in the time domain. A Fourier transformation…
We propose an interferometric method to measure Z2 topological invariants of time-reversal invariant topological insulators realized with optical lattices in two and three dimensions. We suggest two schemes which both rely on a combination of Bloch oscillations with Ramsey interferometry and can be implemented using standard tools of atomic physics. In contrast to topological Zak phase and Chern number, defined for individual 1D and 2D Bloch bands, the formulation of the Z2 invariant involves at least two Bloch bands related by time- reversal symmetry which one has keep track of in measurement…
We propose to investigate the full counting statistics of nonequilibrium spin transport with an ultracold atomic quantum gas. The setup makes use of the spin control available in atomic systems to generate spin transport induced by an impurity atom immersed in a spin-imbalanced two-component Fermi gas. In contrast to solid-state realizations, in ultracold atoms spin relaxation and the decoherence from external sources is largely suppressed. As a consequence, once the spin current is turned off by manipulating the internal spin degrees of freedom of the Fermi system, the nonequilibrium spin pop…
Out-of-time-order correlation functions provide a proxy for diagnosing chaos in quantum systems. We propose and analyze an interferometric scheme for their measurement, using only local quantum control and no reverse time evolution. Our approach utilizes a combination of Ramsey interferometry and the recently demonstrated ability to directly measure Renyi entropies. To implement our scheme, we present a pair of cold-atom-based experimental blueprints; moreover, we demonstrate that within these systems, one can naturally realize the transverse-field Sherrington-Kirkpatrick (TFSK) model, which e…
