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Temperature dependent suppression of intensity noise below thermal fluctuations g (2) (0) < 2 in incoherent quantum dot superluminescent diodes (QDSLDs) has been observed by Blazek et al. in 2011 [1] . First-order temporal correlation properties of QDSLDs have been investigated using quantized treatments [2] and stochastic simulations [3] . We show that the noise suppression can be interpreted as a nonlinear damping effect by considering the interaction between a statistically distributed classical electric field and a pumped atomic three-level-system.

We analyze the transfer function of a three-dimensional atomic Bragg beamsplitter formed by two counterpropagating pulsed Laguerre-Gaussian laser beams. Even for ultracold atomic ensembles, the transfer efficiency depends significantly on the residual velocity of the particles as well as on losses into higher diffraction orders. Additional aberrations are caused by the spatial intensity variation and wavefront curvature of the Laguerre-Gaussian laser beam envelope, studied with (3+1)-dimensional numerical simulations. The temporal pulse shape also affects the transfer efficiency significantly. Thus, we consider the practically important rectangular, Gaussian, Blackman, and hyperbolic secant pulses. For the last, we can describe the time-dependent response analytically with the Demkov-Kunike method. The experimentally observed stretching of the $\ensuremath{\pi}$-pulse time is explained from a renormalization of the simple Pendell\"osung frequency. Finally, we compare the analytical predictions for the velocity-dependent transfer function with effective (1+1)-dimensional numerical simulations for pulsed Laguerre-Gaussian laser beams, as well as experimental data, and find very good agreement considering a mixture of Bose-Einstein condensate and thermal cloud.

Space offers virtually unlimited free-fall in gravity. Bose-Einstein condensation (BEC) enables ineffable low kinetic energies corresponding to pico- or even femtokelvins. The combination of both features makes atom interferometers with unprecedented sensitivity for inertial forces possible and opens a new era for quantum gas experiments. On January 23, 2017, we created Bose-Einstein condensates in space on the sounding rocket mission MAIUS-1 and conducted 110 experiments central to matter-wave interferometry. In particular, we have explored laser cooling and trapping in the presence of large accelerations as experienced during launch, and have studied the evolution, manipulation and interferometry employing Bragg scattering of BECs during the six-minute space flight. In this letter, we focus on the phase transition and the collective dynamics of BECs, whose impact is magnified by the extended free-fall time. Our experiments demonstrate a high reproducibility of the manipulation of BECs on the atom chip reflecting the exquisite control features and the robustness of our experiment. These properties are crucial to novel protocols for creating quantum matter with designed collective excitations at the lowest kinetic energy scales close to femtokelvins., 6 pages, 4 figures

The velocity distribution of a hot ionic beam can be filtered with a narrow stimulated Raman process to prepare a colder subensemble, as substantiated in this theoretical analysis. Using two counter-propagating, far-detuned lasers, we can define a $\pi$-pulse for the resonant velocity to transfer atoms within the linewidth of the Raman resonance between the ground-states of a $\Lambda$-system. Spontaneous emission from the two single-photon resonances, as well as the ground-state decoherence induced by laser noise, diminishes the efficiency of the filter. From a comprehensive master equation, we obtain conditions for the optimal frequency pair of the lasers and evaluate the filter performance numerically, as well as analytically. If we apply this analysis to current $^{40}$Ca$^+$ ion experiments, we obtain a sensitivity for measuring high ion acceleration voltages on the ppm level or below., Comment: Corrected typos. Corrected: Missing minus in Eq. 35. Improved readability by including a few repetitions of quantity definitions and improved display of relevant quantities in Table II of the Appendix

We present a stochastic procedure to investigate the correlation spectra of quantum dot superluminescent diodes. The classical electric field of a diode is formed by a polychromatic superposition of many independent stochastic oscillators. Assuming fields with individual carrier frequencies, Lorentzian linewidths and amplitudes we can form any relevant experimental spectrum using a least square fit. This is illustrated for Gaussian and Lorentzian spectra, Voigt profiles and box shapes. Eventually, the procedure is applied to an experimental spectrum of a quantum dot superluminescent diode which determines the first- and second-order temporal correlation functions of the emission. We find good agreement with the experimental data and a quantized treatment. Thus, a stochastic field represents broadband light emitted by quantum dot superluminescent diodes., Comment: 10 pages, 5 figures

We present a microscopic theory of the amplified spontaneous emission of a spectrally broadband quantum dot superluminescent diode with tilted end facets within the quantum white noise limit. From this multimode quantum theory, we have the ability to obtain all orders of temporal correlation functions. In particular, we derive rate equations for the optical power densities, the level occupation of inhomogeneous ensemble of quantum dots within the diode, as well as the emitted optical spectra. As the main result, we find the external power spectrum as a convolution of the intra-diode photon spectrum with a Lorentzian response. Assuming a Gaussian light-matter coupling results in a similar shaped Gaussian output spectrum, which agrees very well with available experimental data.

We theoretically analyze a scheme for a fast adiabatic transfer of cold atoms from the atomic limit of isolated traps to a Mott-insulator close to the superfluid phase. This gives access to the Bose-Hubbard physics without the need of a prior Bose-Einstein condensate. The initial state can be prepared by combining the deterministic assembly of atomic arrays with resolved Raman sideband cooling. In the subsequent transfer the trap depth is reduced significantly. We derive conditions for the adiabaticity of this process and calculate optimal adiabatic ramp shapes. Using available experimental parameters, we estimate the impact of heating due to photon scattering and compute the fidelity of the transfer scheme. Finally, we discuss the particle number scaling behavior of the method for preparing low-entropy states. Our findings demonstrate the feasibility of the proposed scheme with state-of-the-art technology., Comment: Minor changes based on referee reports

Atom interferometry provides the opportunity of high-precision measurements of rotation and acceleration [1]. Therefore atoms are the ultimate quantum sensors. In the configuration of an atom interferometer they provide the opportunity of high-precision rotation and acceleration sensing. Potential applications range from the further understanding of fundamental physics to inertial navigation and geological exploration. In the QUANTUS freefall experiments atom interferometery is the central method as well [2].

Commercial devices for optical coherence tomography greatly benefit from the appealing features of broadband light emitting quantum dot superluminescent diodes (QDSLDs). Here, light generation occurs at the transition of spontaneous to stimulated emission, the regime of amplified spontaneous emission (ASE), where initially spontaneously emitted photons are amplified by stimulated emission processes during their propagation through the device, enabling strong light amplification. The delicate choice of waveguide geometry and gain medium, here the quantum dots (QDs), enables large spectral widths of some THz (see Fig. 1 (left)) as well as spatial coherence. Modern measurement methods based on detectors [1], which take advantage of the two photon absorption process (TPA), already theoretically predicted by B. R. Mollow in 1968 [2], provide a temporal resolution high enough to detect this radiation with coherence time in the order of fs and permit correlation studies of QDSLDs.

Quantum sensors based on matter-wave interferometry are promising candidates for high-precision gravimetry and inertial sensing in space. The favorable sources for the coherent matter waves in these devices are Bose–Einstein condensates. A reliable prediction of their dynamics, which is governed by the Gross–Pitaevskii equation, requires suitable analytical and numerical methods, which take into account the center-of-mass motion of the condensate, its rotation, and its spatial expansion by many orders of magnitude. In this chapter, we present an efficient way to study their dynamics in time-dependent rotating traps that meet this objective. Both an approximate analytical solution for condensates in the Thomas–Fermi regime and dedicated numerical simulations on a variable adapted grid are discussed. We contrast and relate our approach to previous alternative methods and provide further results, such as analytical expressions for the one- and two-dimensional spatial density distributions and the momentum distribution in the long-time limit that are of immediate interest to experimentalists working in this field of research.

We present a novel platform for the bottom-up construction of itinerant many-body systems: ultracold atoms transferred from a Bose-Einstein condensate into freely configurable arrays of micro-lens generated focused-beam dipole traps. This complements traditional optical lattices and gives a new quality to the field of two-dimensional quantum simulators. The ultimate control of topology, well depth, atom number, and interaction strength is matched by sufficient tunneling. We characterize the required light fields, derive the Bose-Hubbard parameters for several alkali species, investigate the loading procedures and heating mechanisms. To demonstrate the potential of this approach, we analyze coupled annular Josephson contacts exhibiting many-body resonances., Comment: 8 pages, 6 figures

Clouds of ultra-cold atoms and especially Bose–Einstein condensates (BEC) provide a source for coherent matter-waves in numerous earth bound experiments. Analogous to optical interferometry, matter-wave interferometers can be used for precision measurements allowing for a sensitivity orders of magnitude above their optical counterparts. However, in some respects the presence of gravitational forces in the lab limits experimental possibilities. In this article, we report about a compact and robust experiment generating Bose–Einstein condensates in the drop tower facility in Bremen, Germany. We also present the progress of building the succeeding experiment in which a two species atom interferometer will be implemented to test the weak equivalence principle with quantum matter.

Going Down the Tube Two pillars of modern physics are quantum mechanics and general relativity. So far, both have remained apart with no quantum mechanical description of gravity available. Van Zoest et al. (p. 1540 ; see the Perspective by Nussenzveig and Barata ) present work with a macroscopic quantum mechanical system—a Bose-Einstein condensate (BEC) of rubidium atoms in which the cloud of atoms is cooled into a collective quantum state—in microgravity. By dropping the BEC down a 146-meter-long drop chamber and monitoring the expansion of the quantum gas under these microgravity conditions, the authors provide a proof-of-principle demonstration of a technique that can probe the boundary of quantum mechanics and general relativity and perhaps offer the opportunity to reconcile the two experimentally.

Weightlessness promises to substantially extend the science of quantum gases toward presently inaccessible regimes of low temperatures, macroscopic dimensions of coherent matter waves, and enhanced duration of unperturbed evolution. With the long-term goal of studying cold quantum gases on a space platform, we currently focus on the implementation of an 87 Rb Bose–Einstein condensate (BEC) experiment under microgravity conditions at the ZARM drop tower in Bremen (Germany). Special challenges in the construction of the experimental setup are posed by a low volume of the drop capsule (< 1 m3) as well as critical vibrations during capsule release and peak decelerations of up to 50 g during recapture at the bottom of the tower. All mechanical and electronic components have thus been designed with stringent demands on miniaturization, mechanical stability and reliability. Additionally, the system provides extensive remote control capabilities as it is not manually accessible in the tower two hours before and during the drop. We present the robust system and show results from first tests at the drop tower.

We experimentally demonstrate the possibility of preparing ultracold atoms in the environment of weightlessness at the earth-bound short-term microgravity laboratory Drop Tower Bremen, a facility of ZARM – University of Bremen. Our approach is based on a freely falling magneto-optical trap (MOT) drop tower experiment performed within the ATKAT collaboration (“Atom-Catapult”) as a preliminary part of the QUANTUS pilot project (“Quantum Systems in Weightlessness”) pursuing a Bose–Einstein condensate (BEC) in microgravity at the drop tower [1, 2].

We consider Feshbach scattering of fermions in a one-dimensional optical lattice. By formulating the scattering theory in the crystal momentum basis, one can exploit the lattice symmetry and factorize the scattering problem in terms of center-of-mass and relative momentum in the reduced Brillouin zone scheme. Within a single band approximation, we can tune the position of a Feshbach resonance with the center-of-mass momentum due to the non-parabolic form of the energy band.

We report the current status of our cooperative effort to realize a 87Rb Bose–Einstein condensate in microgravity. Targeting the long-term goal of studying cold quantum gases on a space platform, we currently focus on the implementation of an experiment at the ZARM drop tower in Bremen. Fulfilling the technical requirements for operation in this facility, the complete experimental setup will fit in a volume of less than 1 m3 with a total mass below 150 kg and a total power consumption of the order of 625 W. The individual parts of the setup, in particular the ultra-compact laser system as a critical component, are presented. In addition, we discuss a first demonstration of the mechanical and frequency control stability of the laser modules. On the theoretical side, we outline the non-relativistic description of a freely falling many-particle system in the rotating frame of the Earth. In particular, we show that the time evolution of a harmonically trapped, collisionally interacting degenerate gas of bosons or fermions is as simple in an accelerated, rotating frame of reference as in an inertial frame. By adopting a co-moving generalized Galilean frame, we can eliminate inertial forces and torques. This leads to important simplifications for numerical simulation of the experiment.

We analyze the statistics of photons originating from amplified spontaneous emission generated by a quantum dot superluminescent diode. Experimentally detectable emission properties are taken into account by parametrizing the corresponding quantum state as a multi-mode phase-randomized Gaussian density operator. The validity of this model is proven in two subsequent experiments using fast two-photon-absorption detection observing second order equal-time- as well as second order fully time-resolved intensity correlations on femtosecond timescales. In the first experiment, we study the photon statistics when the number of contributing longitudinal modes is systematically reduced by applying well-controlled optical feedback. In a second experiment, we add coherent light from a single-mode laserdiode to quantum dot superluminescent diode broadband radiation. Tuning the power ratio, we realize tailored second order correlations ranging from Gaussian to Poissonian statistics. Both experiments are very well matched by theory, thus giving first insights into quantum properties of radiation from quantum dot superluminescent diodes., submitted to New Journal of Physics

We review the basic concepts of a non-equilibrium kinetic theory of a trapped bosonic gas. By extending the successful mean-field concept of the Gross-Pitaevskii equation with the effects of non-local, two particle quantum correlations, one obtains a renormalized binary interaction and allows for the dynamic establishment of non-classical many-particle quantum correlations. These concepts are illustrated by self-consistent numerical calculations of the first and second order ground state quantum correlations of a harmonically trapped, quasi one-dimensional bosonic gas. We do find a strong suppression of the density fluctuations or, in other words, an enhanced number squeezing with decreasing particle density., 19 pages LaTeX, 19 color figures, to be published in the special issue on "Degenerate Quantum Gases" in Opt. Com. (2004)

We derive a theory of superfluidity for a dilute Fermi gas that is valid when scattering resonances are present. The treatment of a resonance in many-body atomic physics requires a novel mean-field approach starting from an unconventional microscopic Hamiltonian. The mean-field equations incorporate the microscopic scattering physics, and the solutions to these equations reproduce the energy-dependent scattering properties. This theory describes the high-$T_c$ behavior of the system, and predicts a value of $T_c$ which is a significant fraction of the Fermi temperature. It is shown that this novel mean-field approach does not break down for typical experimental circumstances, even at detunings close to resonance. As an example of the application of our theory we investigate the feasibility for achieving superfluidity in an ultracold gas of fermionic $^6$Li., 15 pages, 10 figures

We investigate the feasibility of UV lasing without inversion at a wavelength of $253.7$ nm utilizing interacting dark resonances in mercury vapor. Our theoretical analysis starts with radiation damped optical Bloch equations for all relevant 13 atomic levels. These master equations are generalized by considering technical phase noise of the driving lasers. From the Doppler broadened complex susceptibility we obtain the stationary output power from semiclassical laser theory. The finite overlap of the driving Gaussian laser beams defines an ellipsoidal inhomogeneous gain distribution. Therefore, we evaluate the intra-cavity field inside a ring laser self-consistently with Fourier optics. This analysis confirms the feasibility of UV lasing and reveals its dependence on experimental parameters., changes were made according to reviewer comments (accepted for publication in JOSA B)

The most salient features of the Bose-Einstein condensation of a magnetically confined alkali vapor is the diluteness of the gas and the extremely weak effective interactions. From a theoretical point of view, the interesting aspect is the potential formulation of the many-body quantum theory for a non-uniform and potentially non-equilibrium system founded entirely on microscopic physics. The crucial postulate is the rapid attenuation of many particle quantum correlations in the dilute system which can be motivated from universal considerations. In principle, it will be possible to provide direct comparison between theory and experiment over all temperature scales with no phenomenological parameters — a challenge facing the theoretical community in the near future. The dilute gas experiments provide an exciting stage on which to build bridges linking the theory of complex and collective phenomena in superconducting and superfluid systems, with the single particle microscopic physics described in quantum optics and laser physics.

In this paper, we show that pair-correlations may play an important role in the quantum statistical properties of a Bose-Einstein condensed gas composed of an atomic field resonantly coupled with a corresponding field of molecular dimers. Specifically, pair-correlations in this system can dramatically modify the coherent and incoherent transfer between the atomic and molecular fields., 4 pages, 4 figures

In the usual method of evaporative cooling used so far in Bose-Einstein condensation ~BEC! experiments @1‐6# ,afi nite number of atoms are collected in a magnetic trap after being laser cooled to a phase space density at least five orders of magnitude below the critical density needed for BEC. The frequency of an external RF radiation field, which spinflips the atoms to an untrapped state, is then lowered continuously. This further cools the gas by removing high energy atoms from the tail of the distribution. This evaporative cooling procedure increases the phase space density above the critical point needed to reach BEC. The success of this method is well established experimentally, allowing many fundamental properties of Bose-Einstein condensation to be investigated @7‐12#. This standard method of achieving BEC has one critical drawback: once a condensate has been obtained, it has a finite lifetime in the trap determined by various loss mechanisms, such as collisions with hot atoms from the background gas, and inelastic collisions between the trapped atoms. Although the finite lifetime of the condensate does not prevent many crucial properties of the system to be studied, it is still very desirable to achieve a steady-state situation so that a condensate can be sustained for an indefinite period of time. Such a situation is essential for the continuous output of a coherent beam of atoms in an atom laser @13‐18# .T o date, no experiment has demonstrated a steady-state condensation. We address this problem by constructing an intuitive model describing the two aspects to such an experiment: The continuous loading of atoms into the magnetic trap and the classical kinetic evolution of the trapped atoms toward a steady state during the evaporation. Our description of the loading procedure is based on the experimental setup described in @19#, where the authors loaded a magnetic trap with atoms which had been cooled in a separate MOT. This allows us to estimate the rate g f that atoms enter the trap below the RF cut, as well as the mean energy e f of the injected atoms. To model the classical kinetic evolution, we assume a truncated Boltzmann distribution for the trapped atoms and obtain rate equations for the total number N(t) and energy E(t) of the system @1,3‐6#. These rate equations include the loss of atoms due to elastic collisions with the backgroundgas atoms, inelastic three-body collisions, and evaporation, as well as the gain of atoms due to loading. We then numerically calculate the steady-state solution of these equations and show plots of the peak phase space density r 0 as a function of the various physical parameters of the system. We show that the critical regime r 0>2.612 may be reached in order to obtain BEC in steady state.

Atom interferometers covering macroscopic domains of space-time are a spectacular manifestation of the wave nature of matter. Due to their unique coherence properties, Bose-Einstein condensates are ideal sources for an atom interferometer in extended free fall. In this paper we report on the realization of an asymmetric Mach-Zehnder interferometer operated with a Bose-Einstein condensate in microgravity. The resulting interference pattern is similar to the one in the far-field of a double-slit and shows a linear scaling with the time the wave packets expand. We employ delta-kick cooling in order to enhance the signal and extend our atom interferometer. Our experiments demonstrate the high potential of interferometers operated with quantum gases for probing the fundamental concepts of quantum mechanics and general relativity., Comment: 8 pages, 3 figures; 8 pages of supporting material

We investigate the sympathetic relaxation of a free-standing, vibrating carbon nano-tube that is mounted on an atom chip and is immersed in a cloud of ultra-cold atoms. Gas atoms colliding with the nano-tube excite phonons via a Casimir-Polder potential. We use Fermi's Golden Rule to estimate the relaxation rates for relevant experimental parameters and develop a fully dynamic theory of relaxation for the multi-mode phononic field embedded in a thermal atomic reservoir. Based on currently available experimental data, we identify the relaxation rates as a function of atom density and temperature that are required for sympathetic ground state cooling of carbon nano-tubes., Comment: 12 pages, 3 color eps figures refereed, improved version, to be published in Phys. Rev. A

The theory of general relativity describes macroscopic phenomena driven by the influence of gravity while quantum mechanics brilliantly accounts for microscopic effects. Despite their tremendous individual success, a complete unification of fundamental interactions is missing and remains one of the most challenging and important quests in modern theoretical physics. The STE-QUEST satellite mission, proposed as a medium-size mission within the Cosmic Vision program of the European Space Agency (ESA), aims for testing general relativity with high precision in two experiments by performing a measurement of the gravitational redshift of the Sun and the Moon by comparing terrestrial clocks, and by performing a test of the Universality of Free Fall of matter waves in the gravitational field of Earth comparing the trajectory of two Bose-Einstein condensates of Rb85 and Rb87. The two ultracold atom clouds are monitored very precisely thanks to techniques of atom interferometry. This allows to reach down to an uncertainty in the E\"otv\"os parameter of at least 2x10E-15. In this paper, we report about the results of the phase A mission study of the atom interferometer instrument covering the description of the main payload elements, the atomic source concept, and the systematic error sources., Comment: 21 pages, 5 figures

A method for the experimental reconstruction of the quantum state of motion for a single trapped ion is proposed. It is based on the measurement of the ground state population of the trap after a sudden change of the trapping potential. In particular, we show how the Q function and the quadrature distribution can be measured directly. In an example we demonstrate the principle and analyze the sensibility of the reconstruction process to experimental uncertainties as well as to finite grid limitations. Our method is not restricted to the Lamb-Dicke Limit and works in one or more dimensions., 4 pages, Revtex format, 4 postscript figures, changed typographical errors

We propose to create pairs of semifluxons starting from a flat-phase state in long, optical 0-pi-0 Josephson junctions formed with internal electronic states of atomic Bose-Einstein condensates. In this optical system, we can dynamically tune the length of the pi-junction, the detuning of the optical transition, or the strength of the laser-coupling, to induce transitions from the flat-phase state to such a semifluxon-pair state. Similarly as in superconducting 0-pi-0 junctions, there are two, energetically degenerate semifluxon-pair states. A linear mean-field model with two internal electronic states explains this degeneracy and shows the distinct static field configuration in a phase-diagram of the junction parameters. This optical system offers the possibility to dynamically create a coherent superposition of the distinct semifluxon-pair states and observe macroscopic quantum oscillation., 5 pages latex, 4 eps figures

We present a theoretical study of the localization1 of atoms with an angular momentumJ g=3 toJ e=4 transition (e.g., chromium atoms) in quantized optical molasses created by two counterpropagating linearly polarized laser beams. We study the localization as a function of the potential depth, the angle between the polarizations and the interaction time with the molasses in the low-intensity limit, and discuss the possibility of adiabatic compression and squeezing of the atomic distribution.

We have investigated theoretically the applicability of phase-fluctuating laser fields in saturated absorption spectroscopy. The fluctuations of pump and probe fields are fully correlated if they are derived from the same laser source. Inside the saturable medium, phase fluctuations are converted into intensity noise. This nonlinear mixing modifies the statistics of the transmitted fields. By measuring higher-order correlations one can deduce additional spectroscopic information. Apart from the mean intensity, we have examined the intensity noise and intensity power spectrum of the weak probe field. The resonances of these correlation functions are also unaffected by large inhomogeneous broadening since they are inherently related to the usual saturated absorption dip. We find qualitative agreement with results of a recent experiment employing this technique [D. H. McIntyre et al., Opt. Lett. 18, 1816 (1993)], which demonstrates the advantages of noise spectroscopy using spectrum analyzers.

This paper presents the current status and future prospects of the Space Atom Interferometer project (SAI), funded by the European Space Agency. Atom interferometry provides extremely sensitive and accurate tools for the measurement of inertial forces. Operation of atom interferometers in microgravity is expected to enhance the performance of such sensors. Main goal of SAI is to demonstrate the possibility of placing atom interferometers in space. The resulting drop-tower compatible atom interferometry acceleration sensor prototype is described. Expected performance limits and potential scientific applications in a micro-gravity environment are also discussed., publishedVersion

We show that the time evolution of a thermal phase state of an anharmonic oscillator with logarithmic energy spectrum is intimately connected to the generalized Riemann $\ensuremath{\zeta}$ function $\ensuremath{\zeta}(s,a)$. Indeed, the autocorrelation function at a time $t$ is determined by $\ensuremath{\zeta}(\ensuremath{\sigma}+i\ensuremath{\tau},a)$, where $\ensuremath{\sigma}$ is governed by the temperature of the thermal phase state and $\ensuremath{\tau}$ is proportional to $t$. We use the JWKB method to solve the inverse spectral problem for a general logarithmic energy spectrum; that is, we determine a family of potentials giving rise to such a spectrum. For large distances, all potentials display a universal behavior; they take the shape of a logarithm. However, their form close to the origin depends on the value of the Hurwitz parameter $a$ in $\ensuremath{\zeta}(s,a)$. In particular, we establish a connection between the value of the potential energy at its minimum, the Hurwitz parameter and the Maslov index of JWKB. We compare and contrast exact and approximate eigenvalues of purely logarithmic potentials. Moreover, we use a numerical method to find a potential which leads to exact logarithmic eigenvalues. We discuss possible realizations of Riemann $\ensuremath{\zeta}$ wave-packet dynamics using cold atoms in appropriately tailored light fields.

International audience; Atom interferometry represents a quantum leap in the technology for the ultra-precise monitoring of accelerations and rotations and, therefore, for all the science that relies on the latter quantities. These sensors evolved from a new kind of optics based on matter-waves rather than light-waves and might result in an advancement of the fundamental detection limits by several orders of magnitude. Matter-wave optics is still a young, but rapidly progressing science. The Space Atom Interferometer project (SAI), funded by the European Space Agency, in a multi-pronged approach aims to investigate both experimentally and theoretically the various aspects of placing atom interferometers in space: the equipment needs, the realistically expected performance limits and potential scientific applications in a micro-gravity environment considering all aspects of quantum, relativistic and metrological sciences. A drop-tower compatible prototype of a single-axis atom interferometry accelerometer is under construction. At the same time the team is studying new schemes, e.g. based on degenerate quantum gases as source for the interferometer. A drop-tower compatible atom interferometry acceleration sensor prototype has been designed, and the manufacturing of its subsystems has been started. A compact modular laser system for cooling and trapping rubidium atoms has been assembled. A compact Raman laser module, featuring outstandingly low phase noise, has been realized. Possible schemes to implement coherent atomic sources in the atom interferometer have been experimentally demonstrated.

International audience; Atom interferometry represents a quantum leap in the technology for the ultra-precise monitoring of accelerations and rotations and, therefore, for the science that relies on these quantities. These sensors evolved from a new kind of optics based on matter-waves rather than light-waves and might result in an advancement of the fundamental detection limits by several orders of magnitude. This paper describes the current status of the Space Atom Interferometer project (SAI), funded by the European Space Agency. In a multi-pronged approach, SAI aims to investigate both experimentally and theoretically the various aspects of placing atom interferometers in space: the equipment needs, the realistically expected performance limits and potential scientific applications in a micro-gravity environment considering all aspects of quantum, relativistic and metrological sciences. A drop-tower compatible atom interferometry acceleration sensor prototype has been designed, and the manufacturing of its subsystems has been started. A compact modular laser system for cooling and trapping rubidium atoms has been assembled. A compact Raman laser module, featuring outstandingly low phase noise, has been realized. Possible schemes to implement coherent atomic sources in the atom interferometer have been experimentally demonstrated.

The nonlinear dynamics of a sample of two-level systems exposed to noisy laser light is investigated. As stochastic models we treat the chaotic field and the real Gaussian field. Based on the method of marginal characteristic functions, we deduce analytical solutions for the mean values and variances of the atomic populations in terms of matrix continued fractions. We find significantly enhanced on-resonance fluctuations for a real Gaussian field compared to a chaotic field of the same bandwidth and intensity. Furthermore, in contrast to phase-noise models, the fluctuations in the fluorescence intensity do not decrease to zero in the limit of slow fluctuations.

In this article we present actual projects concerning high resolution measurements developed for future space missions based on ultracold atoms at the Institut für Quantenoptik (IQ) of the University of Hannover. This work involves the realization of a Bose–Einstein condensate in a microgravitational environment and of an inertial atomic quantum sensor.

International audience; In response to ESA's Call for proposals of 5 March 2007 of the COSMIC VISION 2015-2025 plan of the ESA science programme, we propose a M-class satellite mission to test of the Equivalence Principle in the quantum domain by investigating the extended free fall of matter waves instead of macroscopic bodies as in the case of GAUGE, MICROSCOPE or STEP. The satellite, called Matter Wave Explorer of Gravity, will carry an experiment to test gravity, namely the measurement of the equal rate of free fall with various isotopes of distinct atomic species with precision cold atom interferometry in the vicinity of the earth. This will allow for a first quantum test the Equivalence Principle with spin polarised particles and with pure fermionic and bosonic atomic ensembles. Due to the space conditions, the free fall of Rubidium and Potassium isotopes will be compared with a maximum accelerational sensitivity of 5*10 − 16 m/s2 corresponding to an accuracy of the test of the Equivalence Principle of 1 part in 1016. Besides the primary scientific goal, the quantum test of the Equivalence Principle, the mission can be extended to provide additional information about the gravitational field of the earth or for testing theories of fundamental processes of decoherence which are investigated by various theory groups in the context of quantum gravity phenomenology. In this proposal we present in detail the mission objectives and the technical aspects of the proposed mission.

We examine ground state correlations for repulsive, quasi one-dimensional bosons in a harmonic trap. In particular, we focus on the few particle limit N=2, 3, 4, …, where exact numerical solutions of the many particle Schrödinger equation are available, by employing the multi-configuration time-dependent Hartree method. Our numerical results for the inhomogeneous system are modeled with the analytical solution of the homogeneous problem using the Bethe ansatz and the local density approximation. Tuning the interaction strength from the weakly correlated Gross–Pitaevskii to the strongly correlated Tonks–Girardeau regime reveals finite particle number effects in the second-order correlation function beyond the local density approximation., publishedVersion

In the usual method of evaporative cooling used so far in Bose-Einstein condensation ~BEC! experiments @1‐6# ,afi nite number of atoms are collected in a magnetic trap after being laser cooled to a phase space density at least five orders of magnitude below the critical density needed for BEC. The frequency of an external RF radiation field, which spinflips the atoms to an untrapped state, is then lowered continuously. This further cools the gas by removing high energy atoms from the tail of the distribution. This evaporative cooling procedure increases the phase space density above the critical point needed to reach BEC. The success of this method is well established experimentally, allowing many fundamental properties of Bose-Einstein condensation to be investigated @7‐12#. This standard method of achieving BEC has one critical drawback: once a condensate has been obtained, it has a finite lifetime in the trap determined by various loss mechanisms, such as collisions with hot atoms from the background gas, and inelastic collisions between the trapped atoms. Although the finite lifetime of the condensate does not prevent many crucial properties of the system to be studied, it is still very desirable to achieve a steady-state situation so that a condensate can be sustained for an indefinite period of time. Such a situation is essential for the continuous output of a coherent beam of atoms in an atom laser @13‐18# .T o date, no experiment has demonstrated a steady-state condensation. We address this problem by constructing an intuitive model describing the two aspects to such an experiment: The continuous loading of atoms into the magnetic trap and the classical kinetic evolution of the trapped atoms toward a steady state during the evaporation. Our description of the loading procedure is based on the experimental setup described in @19#, where the authors loaded a magnetic trap with atoms which had been cooled in a separate MOT. This allows us to estimate the rate g f that atoms enter the trap below the RF cut, as well as the mean energy e f of the injected atoms. To model the classical kinetic evolution, we assume a truncated Boltzmann distribution for the trapped atoms and obtain rate equations for the total number N(t) and energy E(t) of the system @1,3‐6#. These rate equations include the loss of atoms due to elastic collisions with the backgroundgas atoms, inelastic three-body collisions, and evaporation, as well as the gain of atoms due to loading. We then numerically calculate the steady-state solution of these equations and show plots of the peak phase space density r 0 as a function of the various physical parameters of the system. We show that the critical regime r 0>2.612 may be reached in order to obtain BEC in steady state.

Magneto-optically trapped (in a mirror-MOT) 87Rb atoms have been observed in microgravity during the 4.5 s. flight. Furthermore, the experiment was able to capture 3ldr106 atoms at the temperature of 40 muK in an Ioffe-Pritchard magnetic chip trap. The corresponding phase-space density is of the order of 10-7. Evaporative cooling - the final stage on the way towards BEC - is currently being implemented.

In this proceeding we present ongoing projects concerning high resolution measurements developed for future space missions based on ultracold atoms at the Institut fur Quantenoptik (IQ) of the Leibniz-Universitat Hannover. This work involves the realization of a Bose Einstein condensate in microgravitational environment and an inertial atomic quantum sensor.