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Quantum atom optics

(last update: January 2018)

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Postdoc positon

The quantum atom optics group has a postdoctoral position available. Contact Chris Westbrook for more information.

Introduction

  • The results obtained by our team and detailed below are presented in inverse chronological order.
  • A video page presents examples of videos taken with our 3D single atom detector

OA/He*/sciencebec

Rough sketch of the setup showing the atomic cloud in red, the magnetic coils creating the trapping field on each side in white and, underneath, the micro-channel plate.

Metastable helium, in the 2 3S1 state (denoted hereafter as He*) is a fascinating subject for study in the context of degenerate quantum gases. It has a simple internal atomic structure, an easily accessible near-infrared transition for optical manipulation and, as was demonstrated in our group in 2001 it can undergo Bose-Einstein condensation at micro-K temperatures.

Perhaps the most important feature of He* is its large internal energy which permits direct detection of the atoms using electron multipliers and micro-channel plates (MCP). This large internal energy also causes Penning ionizing collisions (He* + He* → He + He+ +e) between metastable atoms, and the products from these collisions can also be electronically detected. Thus He* provides a new window on quantum degenerate gas phenomena which we have been exploiting in the past several years. Indeed, in almost all of the experiments we have performed to date, data was gathered by electronic detection (an MCP) rather than by optical means.

Results

A two-particle four-mode atom interferometer

Two-Particle Four-Mode Interferometer for Atoms, Dussarrat et al., Phys. Rev. Lett. 119, 1732 (2017), arXiv:1707.01279.

2p4m

We have used a variant of the Hong Ou Mandel setup described below to realize a two-particle interferometer with four input and four output ports as shown in the figure. The source generates atom pairs in a superposition of different momentum states:

|ψ) ~ |p,-p) + |p',-p').

When such a state is injected into the atom interferometer, the probability of detecting an atom at each output port is 1/4, independent of any interferometer phase. The correlations between the different output ports however do vary as a function of the relative phase of the two closed circuits (red and blue in the figure). We have demonstrated this effect in our apparatus. An improved version of this experiment can lead to the violation of a Bell inequality involving the motional degrees of freedom of freely falling massive particles.

Atomic Hong Ou Mandel effect

Tunable source of correlated atoms, M. Bonneau et al. Phys. Rev. A 87, 061603 (2013).

Atomic Hong Ou Mandel effect, R. Lopes et al., Nature 520, 66 (2015) [arXiv preprint] [Nature]

see also Two-atom bunching, L. J. Leblanc, News and Views, Nature 520, 36 (2015) [N&V]

The Hong Ou Mandel (HOM) effect is a remarkable illustration of 2 particle interference. Two identical particles arrive at the input ports of a beam splitter. If they are perfectly overlapped, they never exit in opposite output ports. The effect is well known for photons. We have recently performed the analogous experiment for atoms.

HOMdiagDip-2

On the left is shown a schematic representation of the experiment. a) Correlated pairs of atoms are produced by a scattering process in an optical lattice. b) Trajectories labeled a and b separate and then are brought together again by Bragg scattering at time t2. The trajectories overlap again at time t3 and if another Bragg pulse is applied at that time an HOM interferometer is realized. The figure exaggerates the parabolic trajectories of the atoms. c) Two possible trajectories in which both particles are reflected or transmitted by the beamsplitter are shown. The quantum amplitudes corresponding to these two possibilities cancel causing the coincidence between detectors c and d to vanish. d) On the right is shown the c-d coincidence rate as a function of the time τ when the beamsplitting pulse is applied. When this time corresponds to overlapped trajectories (about 550 μs), the coincidence rate drops dramatically.

Intensity fluctuations of superradiance

Second-order coherence of superradiance from a Bose-Einstein condensate, R. Lopes et al., Phys. Rev. A 90, 013615 (2014)

SuperRadIllust

A BEC has sufficient optical thickness to act as a gain medium. When an elongated BEC is excited by a laser beam, the gain causes the spontaneous emission to be preferentially directed in the elongated direction, in so called endfire modes. Since it involves considerable gain and is highly directional, this emission resembles laser emission. We have measured the intensity (2nd order) correlation function of this emission and found that its statistical properties resemble those of a thermal source rather than those of a laser. We do this by observing the recoil of each atom undergoing a superradiant scattering process. Our detector allows us to construct the 2-atom correlation function and thereby infer the correlation function of the emitted light.

The two figures labeled a) show the momentum distribution of the scattered atoms after scattering a single photon. They therefore reflect the radiation pattern in a plane. The leftmost figure is the distribution corresponding to a dilute medium showing a characteristic dipole radiation pattern (cos2 θ). The next figure is the analogous distribution for a dense BEC elongated in the vertical direction. Strong enhancement of the emission in the endfire modes is visible. The figure labeled b) is a 2-atom correlation function of the scattered atoms. The orange line is for the dilute cloud (no superradiance); the blue line shows the superradiant case. The black dots correspond to a BEC undergoing a stimulated Raman transition. This process preserves the coherence of the BEC. Despite the strong gain, the intensity fluctuations in the superradiant radiation pattern are more nearly thermal than coherent.

Acoustic analog of the dynamical Casimir effect

An acoustic analog to the dynamical Casimir effect in a Bose-Einstein condensate, J.-C. Jaskula et al, Phys. Rev. Lett. 109, 220401 (2012) [HAL preprint] [PRL]

Casimir

The usual dynamical Casimir effect is the production of photon pairs when a mirror is accelerated in the vacuum. What matters is a rapid (non adiabatic) modification of the eigenmodes of the electromagnetic field. We have studied an acoustic analog of this effect : Phonon pairs are produced when the speed of sound of a condensate is varied. When the phonons cross the border of the condensate they transform into actual atoms that we detect after time of flight. The single shot time of flight shown in the picture was obtained when the condensate density is modulated at frequency ωmod. This produced pairs of phonons each having a momentum q such that their energy is ω(q)=ωmod/2. The two sidebands in the picture are such phonons.

Sub-Poissonnian atom number difference and violation of a Cauchy-Schwarz inequality

Violation of the Cauchy-Schwarz Inequality with Matter Waves, K.V. Kheruntsyan et al, Phys. Rev. Lett. 108, 260401 (2012) [arxiv preprint] [PRL]

Sub-Poissonian Number Differences in Four-Wave Mixing of Matter Waves, J.-C. Jaskula et al, Phys. Rev. Lett. 105, 190402 (2010) [HAL preprint] [PRL]

OA/He*/SubPoiss

Left: View of the halo after the collision of two BECs and a subsequent ballistic expansion. (a) The experimental data ploted in momentum space, with each dot corresponding to a detected atom. An example of two correlated zones is shown (red arrows). The number difference between these two zones shows sub–shot-noise fluctuations. Right: Normalized variance of all possible pairs of zones for the halo cut into 16 zones. Sub-shot noise variance is clearly visible on the 8 correlated pairs of zones.

We demonstrate sub-Poissonian number differences in four-wave mixing of Bose-Einstein condensates of metastable helium. The collision between two Bose-Einstein condensates produces a scattering halo populated by pairs of atoms of opposing velocities, which we divide into several symmetric zones. We show that the atom number difference for opposing zones has sub-Poissonian noise fluctuations, whereas that of nonopposing zones is well described by shot noise. The atom pairs produced in a dual number state are well adapted to sub–shot-noise interferometry and studies of Einstein-Podolsky-Rosen–type nonlocality tests.

We also demonstrate that atoms in the scattered halo violate a Cauchy-Schwarz inequality, indicating in a formally different way the non-classical nature of the scattered field.

Phase matching conditions in BEC collisions

Spontaneous Four-Wave Mixing of de Broglie Waves: Beyond Optics, V. Krachmalnicoff et al, Phys. Rev. Lett. 104, 150402 (2010) [HAL preprint] [PRL]

We investigate the atom-optical analog of degenerate four-wave mixing by colliding two Bose-Einstein condensates of metastable helium. The momentum distribution of the scattered atoms is measured in three dimensions. A simple analogy with photon phase matching conditions suggests a spherical final distribution. We find, however, that it is an ellipsoid with radii smaller than the initial collision momenta. Numerical and analytical calculations agree with this and reveal the interplay between many-body effects, mean-field interaction, and the anisotropy of the source condensate.

Spin mixtures and BEC in a dipole trap

Bose-Einstein condensation and spin mixtures of optically trapped metastable helium, G. B. Partridge et al, Phys. Rev. A 81, 053631 (2010) [HAL preprint] [PRA].

OA/He*/PiegeDipolaire

Schematics of the vertical dipole trap (left) and BEC expansion (right)

We report the realization of a Bose-Einstein condensate of He∗ in an all-optical potential. Up to 105 spin-polarized He∗ atoms are condensed in an optical dipole trap formed from a single, focused, vertically propagating far-off-resonance laser beam. The vertical trap geometry is chosen to best match the resolution characteristics of a delay-line anode microchannel plate detector capable of registering single He∗ atoms. Dipole trap: λ=1547 nm, power of 1.5 W, oscillation frequencies of 15 Hz and 2.5 kHz.

We also confirm the instability of certain spin-state combinations of 4He∗ to two-body inelastic processes, which necessarily affects the scope of future experiments using optically trapped spin mixtures. To first order atomic clouds of m=-1 and of m=+1 are stable whereas those of m=0 are unstable (β00 ~ 6 10-10cm3/s). Mixtures of m=0/+1 and 0/-1 are stable to first order and mixtures of -1/+1 are unstable with β-1+1 ~ 6 10-10cm3/s.

Pair correlations in atomic four wave mixing

A. Perrin, H. Chang, V. Krachmalnicoff, M. Schellekens, D. Boiron, A. Aspect and C. I. Westbrook, Observation of atom pairs in spontaneous four-wave mixing of two colliding Bose-Einstein condensates , Phys. Rev. Lett. 99, 150405 (2007) [HAL preprint] [PRL]

A. Perrin, C. M. Savage, D. Boiron, V. Krachmalnicoff, C. I. Westbrook, K. Kheruntsyan, Atomic four-wave mixing via condensate collisions, New Journal of Physics 10 (2008) 045021 [HAL preprint] [NJP]

J. Chwedenczuk, P. Zin, M. Trippenbach, A. Perrin, V. Leung, D. Boiron, C. I. Westbrook, Pair correlations of scattered atoms from two colliding Bose-Einstein Condensates: Perturbative Approach, Phys. Rev. A 78, 5 (2008) 053605 [HAL preprint] [PRA]

In the center of mass frame of a binary collision, the scattered particles come out "back to back" because of momentum conservation. In the language of deBroglie waves, the same process is called spontaneous, four wave mixing and the oppositely directed wave vectors of the outgoing waves is fixed by a phase matching condition.

OA/He*/collision4WM

Left: Each frame represents a 2.4 ms time slice of the atomic cloud as it passes the plane of the detector. Right: 3D reconstruction of the scattering halo generated by the collision of two BECs after time-of-flight. The two colliding condensates are on the equatorial plane of the sphere. The condensates III and IV generated by four-wave-mixing are visibles on the top and the bottom of the sphere.

We have observed such a process by producing two colliding Bose-Einstein condensates using stimulated Raman transitions. A 3D reconstruction of the collision, obtained with our position sensitive detector, is shown in the figure (right). In the left, one sees a spherical shell represented by circles of varying diameter as the halo passes through the detector location. In the mid plane of the sphere one can see two unscattered pancake-shaped condensates I and II. One can also see a third condensate III, produced by imperfect polarization of the Raman beams, and a fourth condensate IV which results from stimulated four wave mixing of condensates I, II and III.

See video page

Using the atom positions, we can study correlation functions for back to back pairs. We have also observed pairs of atoms emitted in the same direction. This is another manifestation of the Hanbury Brown Twiss effect. Although the back to back correlation is easily understood in terms of classical particles, the HBT peak is necessarily an interference phenomenon, and therefore the process is quantum mechanical. The HBT effect here gives us a measure of the size of the pair production region and therefore allows us to confirm that the momentum spread of a back to back pair, is limited chiefly by the uncertainty principle.

Hanbury Brown Twiss effect for fermions

T. Jeltes, J. M. McNamara, W. Hogervorst, W. Vassen, V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect and C. I. Westbrook, Comparison of the Hanbury Brown-Twiss effect for bosons and fermions, Nature 445, 402 (2007) [HAL preprint] [Nature]

In the summer of 2006, we transported our detector to Amsterdam to collaborate with the VU Amesterdam metastable He group there. This group had recently produced a degenerate gas of the fermionic isotope 3He* using sympathetic cooling by 4He*. Much like in our experiment of 2005 in Orsay, we released the cloud of atoms onto the detector which was placed below the trap. The detector gives the arrival times and positions of individual atoms with a quantum efficiency estimated to be 10%. With this information we can plot a histogram of separations in 3D for all the pairs in a cloud. In Amsterdam, it was possible to use the same apparatus to make measurements on both fermions and bosons and clearly show their contrasting behavior. The figure below shows normalized pair separation histograms taken at the same temperature (about 500 nK), for fermions and bosons.

OA/He*/fermions

The fermions show "anti-bunching" (see "dégroupement" for a French version), i.e. a tendency to avoid each other, due purely to quantum statistical effects. Interactions between the atoms are entirely negligible. This antibunching effect is reminiscent of antibunching of photons, but it is different in that the Pauli exclusion principle (or the exchange anti-symmetry of wavefunctions) forbids more than one atom to occupy the same phase space cell, and thus antibunching is unavoidable.

We have also demonstrated that a diverging atomic lens in the form of a blue-detuned, focussed laser beam, can be used to change the size of the atom source as viewed from the detector. Decreasing the effective source size, the lens increases the correlation length at the detector. Since the antibunching contrast is limited by the detector resolution, which is not small compared to the correlation length, the defocussing technique allows us to increase the anti-bunching contrast.

Hanbury Brown and Twiss experiment

M. Schellekens, R. Hoppeler, A. Perrin, J. Viana Gomes, D. Boiron, C. I. Westbrook and A. Aspect, Hanbury Brown Twiss effect for ultracold quantum gases, Science 310, 648 (2005) [HAL preprint] [Science]

In 1956, two Astronomers, Hanbury Brown and Twiss, showed that photons emitted by a thermal light source, such as a sodium lamp or a star, behaved in a surprising way. They showed that those photons tended to arrive in groups despite the chaotic nature of the source. This bunching (see "dégroupement" for a French version) effect was especially surprising since there is no physical interaction between the photons. Later on, this effect was shown to be related to the quantum mechanical nature of those photons. Quantum mechanics separates all particles in two populations: bosons and fermions. These two classes,obey different statistics compared to classical particles. Bose statistics tend to favor configurations in which individual particles end up in a same quantum state (a Bose-Einstein Condensate is one dramatic example), whereas Fermi statistics exclude those configurations.

OA/He*/correlations

The Hanbury Brown and Twiss bunching effect for thermal clouds of (bosonic) He* atoms. The left graph shows the arrival time correlation (converted to position z), the right graph the detector plane correlation.

The combination of our metastable Helium BEC with a position sensitive micro-channel plate detector allowed us to observe this bunching behavior in 3 dimensions. To perform the experiment, we simply released a cloud of ultra-cold atoms from a magnetic trap onto the detector. After their 308ms time of flight, the arrival times and positions of each atom were recorded and the separation of all pairs was computed and histogrammed.

The atom bunching signal corresponds to the bump in the 1st figure at separations less than 1mm in the run at 0.55 microK. The 2nd two dimensional figure shows the correlation function in the plane of the detector. The asymmetry is due to the asymmetry of the spatial distribution of the source.

Three dimensional atom cloud detection

In order to explore atom correlations with the metastable Helium BEC apparatus, the group acquired in 2005 a position sensitive micro-channel plate detector with a delay line anode (from Roentdek). Though very common in particle and nuclear physics, this is the first use in a cold-atom physics experiment. The detector can hand high mean particle rates (up to 10MHz for the delay-line) while measuring position and arrival times of individual particles with good resolutions (230 μm and 1 ns respectively for the moment). This makes the detector particularly suitable for our experimental conditions especially because of our MHz particle rates (for a duration of 20 ms). The detector allows us to reconstruct the atomic cloud on an atom by atom basis.

See video page showing several example of 3D reconstruction.

Here is an example of 3D reconstruction:

OA/He*/Superrad_Piege_dipolaire

Collisional Properties of Metastable Helium

See O. Sirjean, S. Seidelin, J. Gomes, D. Boiron, C. Westbrook, A. Aspect, and G. Shlyapnikov, Ionization rates in a Bose-Einstein condensate of metastable Helium, Phys. Rev. Lett. 89, 220406 (2002) [arXiv preprint: cond-mat/0208108] [PRL].

See S. Seidelin, O. Sirjean, J. Viana Gomes, D. Boiron, C. Westbrook, and A. Aspect, Using ion production to monitor the birth and death of a metastable helium Bose-Einstein condensate, J. Opt. B: Quantum Semiclass. Opt. 5, S112 (2003) [arXiv preprint: cond-mat/0211112] [JOptB].

See S. Seidelin, J. Viana Gomes, R. Hoppeler, O. Sirjean, D. Boiron, A. Aspect, and C. Westbrook, Getting the elastic scattering length by observing inelastic collisions in ultracold metastable helium atom, Phys. Rev. Lett. 93, 090409 (2004) [arXiv preprint: cond-mat/0401217] [PRL].

The observation of BEC of He* hinged, among other things, on the elastic and inelastic collision properties of the atom at micro-K temperatures. Encouraging theoretical predictions existed, but no experimental information was available. The crucial question was whether elastic collisions, characterized by their scattering length a, were sufficiently rapid compared to inelastic processes in a spin polarized sample, involving presumably both two-body and three-body collisions. Conventionally, the two-body collision rate constant is denoted by β, and the three-body rate constant by L. Because of the large internal energy of He*, a significant fraction if not all of the inelastic collisions result in ions which can be detected by a microchannel plate. Thus monitoring of the ion products in a BEC permits a qualitatively new observation of BEC. The figure below shows the detected ion rate during evaporation through BEC. The sudden increase in the ion production rate is due to the increase in density associated with the BEC transition. This type of data also allows one to reproducibly place a cloud near the BEC transition point Tc.

OA/He*/IonRateBEC

Observed ion rate during evaproration. The red curve, showing an abrupt increase, corresponds to evaporation through BEC. The blue curve corresponds to an evaporation ramp which was ended before achieving BEC.

Using clouds at Tc, it is possible to extract values for the inelastic rate constants. Surprisingly, it is also possible to get an accurate estimate of the elastic scattering length from the ionization measurements. The key idea in these measurements is to use the fact that at Tc the density of the sample is well known using the theory for a weakly interacting Bose gas. A second important ingredient is that in a BEC, the chemical potential μ is simply related to the density and the scattering length. Accurate measurements of Tc and μ are possible by observing the expansion of clouds of atoms, either at Tc or in a BEC. The known density estimated at Tc allows one to use the ion rate to get the ionization rate constants and knowing the ionization rate constants, we can get infer the density in a BEC from the ion rate. The BEC density together with the a measurement of the chemical potential finally gives a value for the scattering length, which is independent of the absolute calibration of the MCP.
Our final results are]:

  • a = 11.3 (+2.5,) nm
  • β = 0.9 (+1.7,-0.8) 10-14 cm3/s
  • L = 2.5 (+4.5,-2.7) 10-27 cm6/s

Observation of Bose-Einstein condensation of Helium

A. Robert, O. Sirjean, A. Browaeys, J. Poupard, S. Nowak, D. Boiron, C. I. Westbrook, A. Aspect, A Bose-Einstein condensate of metastable atoms, Science 292, 461 (2001) [Science]

OA/He*/TOF_historique

Time of flight spectrum at different final frequecies of the rf evaporation ramp. The double structure appearing at low rf is a signature of the Bose-Einstein condensation.

We observed a BEC of He* (in the 2 3S1 state) during the evening of 12 February 2001. Our apparatus used a cloverleaf-type magnetic trap with coils placed in re-entrant vacuum flanges. This design allows us to use a microchannel plate 5 cm below the trap to detect the atoms after releasing them from the trap. An example of a single-shot time-of-flight spectrum is shown in the figure. The horizontal axis is the arrival time of the atoms, but the distribution closely corresponds to the spatial profile of the atoms along one of the strong axes of the trap. The red curve shows a fit to the wings of the distribution giving a temperature of 0.7 μK. The condensate peak shown contains about 50 000 atoms. The trap is initially loaded from a MOT with 3 108 atoms and the rf evaporation ramp lasts about 60s.

Older results

  • Observation of thermalizating elastic collisions in a magnetic trap
  • Observation of magnetic trapping
  • Measurements of light assisted Penning ionization
  • Development of an atom funnel for He*

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