Atomic Shot Noise Research Articles

Microwave Electric Field Measurement Based on Electromagnetically-Induced Transparency and Absorption in Atomic Vapor Cell at Room Temperature

The traceability of microwave electric field is measured based on the Rydberg atomic quantum interference effect. The rubidium atomic vapor cell at room temperature is used as the probe, and the Autler-Townes splitting of two-photon electromagnetically-induced transparency, three-photon electromagnetically-induced transparency and three-photon electromagnetically-induced absorption effect are analyzed theoretically. The measurement limit of atomic shot noise is also discussed. This method is not only suitable for the traceability and self-calibration measurement of the microwave electric field but also for the sub-wavelength imaging and vector measurement of the microwave electric field and will provide a reference for further miniaturization and integration of the atomic microwave probe.

Nuclear Magnetic Resonance Gyro: Ultimate Parameters

The fundamental limitations for the basic metrological parameters of the nuclear magnetic resonance gyro (NMRG) are analyzed. The determinant factors limiting its sensitivity, such as atomic projection noise and light shot noise, are considered. Formulas are derived to estimate the ultimate sensitivity of the NMRG and study its dependence on the parameters of the sensitive element. The main causes of NMRG drifts and possible ways to improve its metrological characteristics are discussed.

Detecting Friedel oscillations in ultracold Fermi gases

Investigating Friedel oscillations in ultracold gases would complement the studies performed on solid state samples with scanning-tunneling microscopes. In atomic quantum gases interactions and external potentials can be tuned freely and the inherently slower dynamics allow to access non-equilibrium dynamics following a potential or interaction quench. Here, we examine how Friedel oscillations can be observed in current ultracold gas experiments under realistic conditions. To this aim we numerically calculate the amplitude of the Friedel oscillations which are induced by a potential barrier in a 1D Fermi gas and compare it to the expected atomic and photonic shot noise in a density measurement. We find that to detect Friedel oscillations the signal from several thousand one-dimensional systems has to be averaged. However, as up to 100 parallel one-dimensional systems can be prepared in a single run with present experiments, averaging over about 100 images is sufficient.Graphical abstract

Sub-atom shot noise Faraday imaging of ultracold atom clouds

We demonstrate that a dispersive imaging technique based on the Faraday effect can measure the atom number in a large, ultracold atom cloud with a precision below the atom shot noise level. The minimally destructive character of the technique allows us to take multiple images of the same cloud, which enables sub-atom shot noise measurement precision of the atom number and allows for an in situ determination of the measurement precision. We have developed a noise model that quantitatively describes the noise contributions due to photon shot noise in the detected light and the noise associated with single atom loss. This model contains no free parameters and is calculated through an analysis of the fluctuations in the acquired images. For clouds containing atoms, we achieve a precision more than a factor of two below the atom shot noise level.

Coherence Times of Bose-Einstein Condensates beyond the Shot-Noise Limit via Superfluid Shielding.

We demonstrate a new way to extend the coherence time of separated Bose-Einstein condensates that involves immersion into a superfluid bath. When both the system and the bath have similar scattering lengths, immersion in a superfluid bath cancels out inhomogeneous potentials either imposed by external fields or inherent in density fluctuations due to atomic shot noise. This effect, which we call superfluid shielding, allows for coherence lifetimes beyond the projection noise limit. We probe the coherence between separated condensates in different sites of an optical lattice by monitoring the contrast and decay of Bloch oscillations. Our technique demonstrates a new way that interactions can improve the performance of quantum devices.

Recent progress in optically-pumped cesium beam clock at Peking University

A compact, long-life, and low-drift cesium beam clock is investigated at Peking University, where the atoms are magnetic-state selected and optically detected. Stability close to that of the best commercial cesium clocks has been achieved from 10 to 105 s. As previously shown, the short-term stability is determined by atomic shot noise or laser frequency noise. The stabilizations of microwave power and C-field improve the long-term stability, with the help of a digital servo system based on field-programmable gate array.

Collective excitation interferometry with a toroidal Bose-Einstein condensate

The precision of compact inertial sensing schemes using trapped- and guided-atom interferometers has been limited by uncontrolled phase errors caused by trapping potentials and interactions. Here, we propose an acoustic interferometer that uses sound waves in a toroidal Bose-Einstein condensate to measure rotation, and we demonstrate experimentally several key aspects of this type of interferometer. We use spatially patterned light beams to excite counter-propagating sound waves within the condensate and use \emph{in situ} absorption imaging to characterize their evolution. We present an analysis technique by which we extract separately the oscillation frequencies of the standing-wave acoustic modes, the frequency splitting caused by static imperfections in the trapping potential, and the characteristic precession of the standing-wave pattern due to rotation. Supported by analytic and numerical calculations, we interpret the noise in our measurements, which is dominated by atom shot noise, in terms of rotation noise. While the noise of our acoustic interferometric sensor, at the level of $\sim \mbox{rad}\, \mbox{s}^{-1}/\sqrt{\mbox{Hz}}$, is high owing to rapid acoustic damping and the small radius of the trap, the proof-of-concept device does operate at $10^4 - 10^6$ times higher density and in a volume $10^9$ times smaller than free-falling atom interferometers.

Stability enhancement by joint phase measurements in a single cold atomic fountain

We propose a method of joint interrogation in a single atom interferometer which overcomes the dead time between consecutive measurements in standard cold atomic fountains. The joint operation enables for a faster averaging of the Dick effect associated with the local oscillator noise in clocks and with vibration noise in cold atom inertial sensors. Such an operation allows one to achieve the lowest stability limit due to atom shot noise. We demonstrate a multiple joint operation in which up to five clouds of atoms are interrogated simultaneously in a single setup. The essential feature of multiple joint operation, demonstrated here for a microwave Ramsey interrogation, can be generalized to go beyond the current stability limit associated with dead times in present-day cold atom interferometer inertial sensors.

A low phase noise microwave frequency synthesis for a high-performance cesium vapor cell atomic clock.

We report the development, absolute phase noise, and residual phase noise characterization of a 9.192 GHz microwave frequency synthesis chain devoted to be used as a local oscillator in a high-performance cesium vapor cell atomic clock based on coherent population trapping (CPT). It is based on frequency multiplication of an ultra-low phase noise 100 MHz oven-controlled quartz crystal oscillator using a nonlinear transmission line-based chain. Absolute phase noise performances of the 9.192 GHz output signal are measured to be -42, -100, -117 dB rad(2)/Hz and -129 dB rad(2)/Hz at 1 Hz, 100 Hz, 1 kHz, and 10 kHz offset frequencies, respectively. Compared to current results obtained in a state-of-the-art CPT-based frequency standard developed at LNE-SYRTE, this represents an improvement of 8 dB and 10 dB at f = 166 Hz and f = 10 kHz, respectively. With such performances, the expected Dick effect contribution to the atomic clock short term frequency stability is reported at a level of 6.2 × 10(-14) at 1 s integration time, that is a factor 3 higher than the atomic clock shot noise limit. Main limitations are pointed out.

Fluorescence detection at the atom shot noise limit for atom interferometry

Atom interferometers (AIs) are promising tools for precision measurement with applications ranging from geophysical exploration and tests of the equivalence principle of general relativity to the detection of gravitational waves. Their optimal sensitivity is ultimately limited by their detection noise. We review resonant and near-resonant methods to detect the atom number of the interferometer outputs, and we theoretically analyze the relative influence of various scheme dependent noise sources and the technical challenges affecting the detection. We show that for the typical conditions under which an AI operates, simultaneous fluorescence detection with a charge-coupled device sensor is the optimal imaging scheme. We extract the laser beam parameters such as detuning, intensity, and duration required for reaching the atom shot noise limit.

Comparison of Atom Interferometers and Light Interferometers as Space-Based Gravitational Wave Detectors

We consider a class of proposed gravitational-wave detectors based on multiple atomic interferometers separated by large baselines and referenced by common laser systems. We compute the sensitivity limits of these detectors due to intrinsic phase noise of the light sources, noninertial motion of the light sources, and atomic shot noise and compare them to sensitivity limits for traditional light interferometers. We find that atom interferometers and light interferometers are limited in a nearly identical way by intrinsic phase noise and that both require similar mitigation strategies (e.g., multiple-arm instruments) to reach interesting sensitivities. The sensitivity limit from motion of the light sources is slightly different and, in principle, favors the atom interferometers in the low-frequency limit, although the limit in both cases is severe.

Detection of small atom numbers through image processing

We demonstrate improved detection of small trapped atomic ensembles through advanced post-processing and optimal analysis of absorption images. A fringe removal algorithm reduces imaging noise to the fundamental photon-shot-noise level and proves beneficial even in the absence of fringes. A maximum-likelihood estimator is then derived for optimal atom-number estimation and is applied to real experimental data to measure the population differences and intrinsic atom shot-noise between spatially separated ensembles each comprising between 10 and 2000 atoms. The combined techniques improve our signal-to-noise by a factor of 3, to a minimum resolvable population difference of 17 atoms, close to our ultimate detection limit.

High-stability compact atomic clock based on isotropic laser cooling

We present a compact cold-atom clock configuration where isotropic laser cooling, microwave interrogation, and clock signal detection are successively performed inside a spherical microwave cavity. For ground operation, a typical Ramsey fringe width of 20 Hz has been demonstrated, limited by the atom cloud's free fall in the cavity. The isotropic cooling light's disordered properties provide a large and stable number of cold atoms, leading to a high signal-to-noise ratio limited by atomic shot noise. A relative frequency stability of $2.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$ has been achieved, averaged down to $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ after $5\ifmmode\times\else\texttimes\fi{}{10}^{3}$ s of integration. Development of such a high-performance compact clock is of major relevance for on-board applications, such as satellite-positioning systems. As a cesium clock, it opens the door to a new generation of compact primary standards and timekeeping devices.

Enhanced and Reduced Atom Number Fluctuations in a BEC Splitter

We measure atom number statistics after splitting a gas of ultracold 87Rb atoms in a purely magnetic double-well potential created on an atom chip. Well below the critical temperature for Bose-Einstein condensation Tc, we observe reduced fluctuations down to -4.9 dB below the atom shot noise level. Fluctuations rise to more than +3.8 dB close to Tc, before reaching the shot noise level for higher temperatures. We use two-mode and classical field simulations to model these results. This allows us to confirm that the supershot noise fluctuations directly originate from quantum statistics.

Local Observation of Antibunching in a Trapped Fermi Gas

Local density fluctuations and density profiles of a Fermi gas are measured insitu and analyzed. In the quantum degenerate regime, the weakly interacting 6Li gas shows a suppression of the density fluctuations compared to the nondegenerate case, where atomic shot noise is observed. This manifestation of antibunching is a direct result of the Pauli principle and constitutes a local probe of quantum degeneracy. We analyze our data using the predictions of the fluctuation-dissipation theorem and the local density approximation, demonstrating a fluctuation-based temperature measurement.

Suppression of Density Fluctuations in a Quantum Degenerate Fermi Gas

We study density profiles of an ideal Fermi gas and observe Pauli suppression of density fluctuations (atom shot noise) for cold clouds deep in the quantum degenerate regime. Strong suppression is observed for probe volumes containing more than 10 000 atoms. Measuring the level of suppression provides sensitive thermometry at low temperatures. After this method of sensitive noise measurements has been validated with an ideal Fermi gas, it can now be applied to characterize phase transitions in strongly correlated many-body systems.

An atomic-resolution nanomechanical mass sensor

Mechanical resonators are widely used as inertial balances to detect small quantities of adsorbed mass through shifts in oscillation frequency. Advances in lithography and materials synthesis have enabled the fabrication of nanoscale mechanical resonators, which have been operated as precision force, position and mass sensors. Here we demonstrate a room-temperature, carbon-nanotube-based nanomechanical resonator with atomic mass resolution. This device is essentially a mass spectrometer with a mass sensitivity of 1.3 x 10(-25) kg Hz(-1/2) or, equivalently, 0.40 gold atoms Hz(-1/2). Using this extreme mass sensitivity, we observe atomic mass shot noise, which is analogous to the electronic shot noise measured in many semiconductor experiments. Unlike traditional mass spectrometers, nanomechanical mass spectrometers do not require the potentially destructive ionization of the test sample, are more sensitive to large molecules, and could eventually be incorporated on a chip.

Squeezing and entanglement of a Bose-Einstein condensate in optical lattices

The squeezing and entanglement properties of a one-component Bose-Einstein condensate trapped in optical lattices are theoretically studied. A two-mode squeezing parameter for the system is found, which is identical with Einstein-Podolsky-Rosen correlation, indicating the quantum correlation between excitation modes. Its dynamics and relation to the Hamiltonian parameters are quantitatively shown, and some constructive relation between squeezing and condensation is pointed out. For entanglement, the entanglement of formation of the two-mode system is also presented. For the probing of such a correlation, relevant experimental issues about atom shot noise are also discussed.

Mott-Insulator Transition in a Two-Dimensional Atomic Bose Gas

Cold atoms in periodic potentials are versatile quantum systems for implementing simple models prevalent in condensed matter theory. Here we realize the 2D Bose-Hubbard model by loading a Bose-Einstein condensate into an optical lattice, and study the resulting Mott insulator. The measured momentum distributions agree quantitatively with theory (no adjustable parameters). In these systems, the Mott insulator forms in a spatially discrete shell structure which we probe by focusing on correlations in atom shot noise. These correlations show a marked dependence on the lattice depth, consistent with the changing size of the insulating shell expected from simple arguments.

Detecting multiatomic composite states in optical lattices

We propose and discuss methods for detecting quasi-molecular complexes which are expected to form in strongly interacting optical lattice systems. Particular emphasis is placed on the detection of composite fermions forming in Bose-Fermi mixtures. We argue that, as an indirect indication of the composite fermions and a generic consequence of strong interactions, periodic correlations must appear in the atom shot noise of bosonic absorption images, similar to the bosonic Mott insulator [S. F\"olling, et al., Nature {\bf 434}, 481 (2005)]. The composites can also be detected directly and their quasi-momentum distribution measured. This method -- an extension of the technique of noise correlation interferometry [E. Altman et al., Phys. Rev. A {\bf 79}, 013603 (2004)] -- relies on measuring higher order correlations between the bosonic and fermionic shot noise in the absorption images. However, it fails for complexes consisting of more than three atoms.