Atom Number Fluctuations Research Articles

Interferometry with independently prepared Bose-Einstein condensates

We show that it is possible to reach the sub shot-noise sensitivity of the phase estimation using two independently prepared Bose-Einstein condensates as an input of an interferometer. In this scenario, the quantum correlations between the particles, which are necessary to beat the shot-noise limit, arise from the indistinguishability of bosons. Allowing for atom number fluctuations independently in each condensate, we calculate the ultimate bound of the sensitivity. Our main conclusion is that even in presence of major atom number fluctuations, an interferometer operating on two independent condensates can give very high sensitivity. We also show that the estimation from the measurement of the number of atoms utilizes these quantum correlations. This observation, in context of recent measurement of the Fisher information in a many-body system [H. Strobel {\it et al}, Science {\bf 345}, 424 (2014)], opens the way towards the construction of a new type of an interferometer operating below the shot-noise limit.

Proposal for the creation and optical detection of spin cat states in Bose-Einstein condensates.

We propose a method to create "spin cat states," i.e., macroscopic superpositions of coherent spin states, in Bose-Einstein condensates using the Kerr nonlinearity due to atomic collisions. Based on a detailed study of atom loss, we conclude that cat sizes of hundreds of atoms should be realistic. The existence of the spin cat states can be demonstrated by optical readout. Our analysis also includes the effects of higher-order nonlinearities, atom number fluctuations, and limited readout efficiency.

Atom-number fluctuation and macroscopic quantum entanglement in dipole spinor condensates

We study the spin distribution and macroscopic entanglement in spinor condensates confined in an anisotropic potential under external magnetic fields. Different types of magnetic phases can be reached by tuning the magnetic dipolar interaction strength by modifying the trapping geometry. We investigate the atom-number fluctuations of the ground state and show that the different internal hyperfine states exhibit super-Poissonian, Poissonian, and sub-Poissonian distributions with different trapping geometries and strengths of the external magnetic field. We also propose a scheme to create a macroscopic maximally entangled spin state by slowly sweeping the external magnetic field.

Atomic Fock State Preparation Using Rydberg Blockade

We use coherent excitation of 3-16 atom ensembles to demonstrate collective Rabi flopping mediated by Rydberg blockade. Using calibrated atom number measurements, we quantitatively confirm the expected √N Rabi frequency enhancement to within 4%. The resulting atom number distributions are consistent with an essentially perfect blockade. We then use collective Rabi π pulses to produce N=1, 2 atom number Fock states with fidelities of 62% and 48%, respectively. The N=2 Fock state shows the collective Rabi frequency enhancement without corruption from atom number fluctuations.

Fingerprinting Rotons in a Dipolar Condensate: Super-Poissonian Peak in the Atom-Number Fluctuations

We demonstrate that measurements of atom-number fluctuations in a trapped dipolar condensate can reveal the presence of the elusive roton excitation. The key signature is a super-Poissonian peak in the fluctuations as the size of the measurement cell is varied, with the maximum occurring when the size is comparable to the roton wavelength. The magnitude of this roton feature is enhanced with temperature. The variation in fluctuations across the condensate demonstrates that the roton excitations are effectively confined to propagate in the densest central region, realizing a density trapped roton gas. While our main results are based on full numerical solutions of the mean-field equations, we also develop and validate a simple local density theory. Finally, we consider fluctuations measured within a washer-shaped cell which filters out the contribution of modes with nonzero angular momentum and provides a signal sensitive to individual roton modes.

Shaking the entropy out of a lattice: Atomic filtering by vibrational excitations

We present a simple and efficient scheme to reduce atom-number fluctuations in optical lattices. The interaction-energy difference for atoms in different vibrational states is used to remove excess atomic occupation. The remaining vacant sites are then filled with atoms by merging adjacent wells, for which we implement a protocol that circumvents the constraints of unitarity. The preparation of large regions with precisely one atom per lattice site is discussed for both bosons and fermions. The resulting low-entropy Mott-insulating states may serve as high-fidelity register states for quantum computing and as a starting point for investigations of many-body physics.

Direct Observation of Quantum Phonon Fluctuations in a One-Dimensional Bose Gas

We report the first direct observation of collective quantum fluctuations in a continuous field. Shot-to-shot atom number fluctuations in small subvolumes of a weakly interacting, ultracold atomic 1D cloud are studied using in situ absorption imaging and statistical analysis of the density profiles. In the cloud centers, well in the quantum quasicondensate regime, the ratio of chemical potential to thermal energy is μ/k(B)T≃4, and, owing to high resolution, up to 20% of the microscopically observed fluctuations are quantum phonons. Within a nonlocal analysis at variable observation length, we observe a clear deviation from a classical field prediction, which reveals the emergence of dominant quantum fluctuations at short length scales, as the thermodynamic limit breaks down.

Fragmentation, domain formation and atom number fluctuations of a two-species Bose–Einstein condensate in an optical lattice

We theoretically study the loading of a two-species Bose–Einstein condensate to an optical lattice in a tightly confined one-dimensional trap. Due to quantum fluctuations, the relative inter- and intra-species phase coherence between the atoms and the on-site atom number fluctuations are reduced in the miscible regime. For the immiscible case the fluctuations are enhanced and the atoms form metastable interleaved spatially separated domains where the domain length and its fluctuations are affected by quantum fluctuations.

Half-vortex unbinding and Ising transition in constrained superfluids

We analyze the thermodynamics of the atomic and (nematic) pair superfluids appearing in the attractive two-dimensional Bose-Hubbard model with a three-body hard-core constraint that has been derived as an effective model for cold atoms subject to strong three-body losses in optical lattices. We show that the thermal disintegration of the pair superfluidity is governed by the proliferation of fractional half-vortices leading to a Berezinskii-Kosterlitz-Thousless transition with unusual jump in the helicity modulus. In addition to the (conventional) Berezinskii-Kosterlitz-Thousless transition out of the atomic superfluid, we furthermore identify a direct thermal phase transition separating the pair and the atomic superfluid phases, and show that this transition is continuous with critical scaling exponents consistent with those of the two-dimensional Ising universality class. We exhibit a direct connection between the partial loss of quasi long-range order at the Ising transition between the two superfluids and the parity selection in the atomic winding number fluctuations that distinguish the atomic from the pair superfluid.

Sub-Poissonian atom-number fluctuations using light-assisted collisions

We investigate experimentally the number statistics of a mesoscopic ensemble of cold atoms in a microscopic dipole trap loaded from a magneto-optical trap and find that the atom-number fluctuations are reduced with respect to a Poisson distribution due to light-assisted two-body collisions. For numbers of atoms $N\ensuremath{\gtrsim}2$, we measure a reduction factor (Fano factor) of $0.72\ifmmode\pm\else\textpm\fi{}0.07$, which differs from 1 by more than four standard deviations. We analyze this fact by a general stochastic model describing the competition between the loading of the trap from a reservoir of cold atoms and multiatom losses, leading to a master equation. Applied to our experimental regime, this model indicates an asymptotic value of $3/4$ for the Fano factor at large $N$ and in the steady state. We thus show that we have reached the ultimate level of reduction in number fluctuations in our system.

Local atom-number fluctuations in quantum gases at finite temperature

We investigate the number fluctuations in small cells of quantum gases pointing out important deviations from the thermodynamic limit fixed by the isothermal compressibility. Both quantum and thermal fluctuations in weakly as well as highly compressible fluids are considered. For the two-dimensional (2D) superfluid Bose gas we find a significant quenching of fluctuations with respect to the thermodynamic limit, in agreement with recent experimental findings. An enhancement of the thermal fluctuations is instead predicted for the 2D dipolar superfluid Bose gas, which becomes dramatic when the size of the sample cell is of the order of the wavelength of the rotonic excitation induced by the interaction.

Local and spatially extended sub-Poisson atom-number fluctuations in optical lattices

We demonstrate that ultracold interacting bosonic atoms in an optical lattice show sub-Poissonian on-site and inter-site atom number fluctuations. The experimental observations agree with numerical predictions of the truncated Wigner approximation. The correlations persist in the presence of multi-mode atom dynamics and even over large spatially extended samples involving several sites and large populations.

Sub-Poissonian Fluctuations in a 1D Bose Gas: From the Quantum Quasicondensate to the Strongly Interacting Regime

We report on local, in situ measurements of atom number fluctuations in slices of a one-dimensional Bose gas on an atom chip setup. By using current modulation techniques to prevent cloud fragmentation, we are able to probe the crossover from weak to strong interactions. For weak interactions, fluctuations go continuously from super- to sub-Poissonian as the density is increased, which is a signature of the transition between the subregimes where the two-body correlation function is dominated, respectively, by thermal and quantum contributions. At stronger interactions, the super-Poissonian region disappears, and the fluctuations go directly from Poissonian to sub-Poissonian, as expected for a "fermionized" gas.

Optimal Control Technique for Many-Body Quantum Dynamics

We present an efficient strategy for controlling a vast range of nonintegrable quantum many-body one-dimensional systems that can be merged with state-of-the-art tensor network simulation methods such as the density matrix renormalization group. To demonstrate its potential, we employ it to solve a major issue in current optical-lattice physics with ultracold atoms: we show how to reduce by about 2 orders of magnitude the time needed to bring a superfluid gas into a Mott insulator state, while suppressing defects by more than 1 order of magnitude as compared to current experiments [T. Stöferle et al., Phys. Rev. Lett. 92, 130403 (2004)]. Finally, we show that the optimal pulse is robust against atom number fluctuations.

Cavity-aided magnetic resonance microscopy of atomic transport in optical lattices

Magnetic resonance imaging (MRI) is a powerful technique for investigating the microscopic properties and dynamics of physical systems. In this work we demonstrate state-sensitive MRI of ultracold atoms in an optical lattice. Single-shot spatial resolution is 120 nm, well below the lattice spacing, and number sensitivity is +/-2.4 for 150 atoms on a single site, well below Poissonian atom-number fluctuations. We achieve this by combining high-spatial-resolution control over the atomic spin using an atom chip, together with nearly quantum-limited spin measurement, obtained by dispersively coupling the atoms to light in a high-finesse optical cavity. The MRI is minimally disruptive of the atoms' internal state, preserving the magnetisation of the gas for subsequent experiments. Using this technique, we observe the nonequilibrium transport dynamics of the atoms among individual lattice sites. We see the atom cloud initially expand ballistically, followed by the onset of interaction-inhibited transport.

Probing Three-Body Correlations in a Quantum Gas Using the Measurement of the Third Moment of Density Fluctuations

We perform measurements of the third moment of atom number fluctuations in small slices of a very elongated weakly interacting degenerate Bose gas. We find a positive skewness of the atom number distribution in the ideal gas regime and a reduced skewness compatible with zero in the quasicondensate regime. For our parameters, the third moment is a thermodynamic quantity whose measurement constitutes a sensitive test of the equation of state, and our results are in agreement with a modified Yang-Yang thermodynamic prediction. Moreover, we show that the measured skewness reveals the presence of true three-body correlations in the system.

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.

Atomic-number fluctuations in a mixture of condensates

We study particle number fluctuations in the quantum ground states of a mixture of two spin-1 atomic condensates when the interspecies spin-exchange coupling interaction $c_{12}\beta$ is adjusted. The two spin-1 condensates forming the mixture are respectively ferromagnetic and polar in the absence of an external magnetic (B-) field. We categorize all possible ground states using the angular momentum algebra and compute their characteristic atom number fluctuations, focusing especially on the the AA phase (when $ c_{12}\beta >0$), where the ground state becomes fragmented and atomic number fluctuations exhibit drastically different features from a single stand alone spin-1 polar condensate. Our results are further supported by numerical simulations of the full quantum many-body system.

Sub-Poissonian Atom-Number Fluctuations by Three-Body Loss in Mesoscopic Ensembles

We show that three-body loss of trapped atoms leads to sub-Poissonian atom-number fluctuations. We prepare hundreds of dense ultracold ensembles in an array of magnetic microtraps which undergo rapid three-body decay. The shot-to-shot fluctuations of the number of atoms per trap are sub-Poissonian, for ensembles comprising 50-300 atoms. The measured relative variance or Fano factor F=0.53+/-0.22 agrees very well with the prediction by an analytic theory (F=3/5) and numerical calculations. These results will facilitate studies of quantum information science with mesoscopic ensembles.

Optimal control of number squeezing in trapped Bose-Einstein condensates

We theoretically analyze atom interferometry based on trapped ultracold atoms and employ optimal control theory in order to optimize number squeezing and condensate trapping. In our simulations, we consider a setup where the confinement potential is transformed from a single to a double well, which allows us to split the condensate. To avoid in the ensuing phase-accumulation stage of the interferometer dephasing due to the nonlinear atom-atom interactions, the atom-number fluctuations between the two wells should be sufficiently low. We show that low number fluctuations (high number squeezing) can be obtained by optimized splitting protocols. Two types of solutions are found: in the Josephson regime we find an oscillatory tunnel control and a parametric amplification of number squeezing, while in the Fock regime squeezing is obtained solely due to the nonlinear coupling, which is transformed to number squeezing by peaked tunnel pulses. We study splitting and squeezing within the frameworks of a generic two-mode model, which allows us to study the basic physical mechanisms and the multiconfigurational time-dependent Hartree for bosons method, which allows for a microscopic modeling of the splitting dynamics in realistic experiments. Both models give similar results, thus highlighting the general nature of these two solution schemes. We finally analyze our results in the context of atom interferometry.