Experiments with ultracold atomic gases Andrey Turlapov Institute of Applied Physics, Russian Academy of Sciences Nizhniy Novgorod

How ultracold Fermi atoms are related to nuclear physics ? The atoms are fermions With the atoms, one may see major Fermi phenomena (as in other Fermi systems): Fermi statistics; Cooper pairing and superfluidity + strong interactions, i.e. Uint ~ EF One may see even more with the atoms (the phenomena unobserved in the other Fermi systems) BEC-to-BCS crossover, i.e. crossover between a gas of Fermi atoms and a gas of diatomic Bose molecules; stability of a resonantly interacting matter; resonant superfluidity; viscosity at the lowest quantum bound (???); itinerant ferromagnetism (???).

Good about atoms: Bad about atoms: Fundamentally no impurities Control over interactions: tunable s-wave collisions somewhat tunable p-wave collisions dipole-dipole collisions (perspective) Tunable spin composition, more than 2 spins Tunable energy, temperature, density Tunable dimensionality (2D – at Nizhniy Novgorod) Direct imaging Bad about atoms: Small particle number (N = 102 – 106 << NAvogadro) Non-uniform matter (in parabolic potential) Coarse temperature tuning (dT > EF/20 as opposed to dT ~ EF/105 in solid-state-physics experiments) No p-wave (and higher) collisions in thermal equilibrium

Ground state splitting in high B Fermions: 6Li atoms Ground state splitting in high B 2p 670 nm 2s Electronic ground state: 1s22s1 Nuclear spin: I=1

Optical dipole trap Laser: P = 100 W llaser=10.6 mm Trap: U ~ 0 – 1 mK Trapping potential of a focused laser beam: Laser: P = 100 W llaser=10.6 mm Trap: U ~ 0 – 1 mK The dipole potential is nearly conservative: 1 photon absorbed per 30 min b/c llaser=10.6 mm >> llithium=0.67 mm

w /2p =(wx wy wz)1/3 /2p ~few kHz Fermi degeneracy Fermi energy: At T=0: Optical dipole trap: w /2p =(wx wy wz)1/3 /2p ~few kHz Natoms=200 000 EF ~ 100 nK - 10 mK Focus of a CO2 laser: 700 x 50 x 50 mm3 Phase space density: r = Natoms / Nstates = 1

2-body strong interactions in a dilute gas (3D) L = 10 000 bohr R=10 bohr ~ 0.5 nm At low kinetic energy, only s-wave scattering (l=0). For l=1, the centrifugal barrier ~ 1 mK >> typical energy ~ 1 mK s-wave scattering length a is the only interaction parameter (for R<< a) Physically, only a/L matters

Scattering in 1-channel model V(r) r R r R V(r) a < 0 ( | a| > >R ) Attractive mean field a > 0 (a > >R) Repulsive mean field The mean field (for weak interactions):

Fano – Feshbach resonance Singlet 2-body potential: electron spins ↑↓ Triplet 2-body potential: electron spins ↓↓

Fano – Feshbach resonance: Zero-energy scattering length a vs magnetic field B 5000 834 gauss 2500 a, bohr 200 400 600 800 1000 1200 1400 1600 528 gauss -2500 -5000 -7500 В, gauss

Instability of the a>0 region towards molecular formation 200 400 600 800 1000 1200 1400 1600 2500 5000 -5000 -2500 -7500 Singlet 2-body potential: electron spins ↑↓ a, bohr Triplet 2-body potential: electron spins ↓↓ В, gauss

BCS-to-BEC crossover a, bohr BEC BCS of Li2 s/fluid 200 400 600 800 1000 1200 1400 1600 2500 5000 -5000 -2500 -7500 BEC of Li2 BCS s/fluid Singlet 2-body potential: electron spins ↑↓ a, bohr Triplet 2-body potential: electron spins ↓↓ В, gauss

Resonant s-wave interactions (a → ± ∞) Is the mean field ? ? Energy balance at a → - ∞: Collapse s-wave scattering amplitude: In a Fermi gas k≠0. k~kF. Therefore, at a =∞,

Universality L R -V0 Compare with neutron matter: a = –18 fm, R = 2 fm Strong interactions: |a|>L>>R At a→∞, the system is universal, i.e., L is the only length scale: - No dependence on microscopic details of binary interactions - All local properties depend only on n and T -V0 R Experiment (sound propagation, Duke, 2007): b = - 0.565(.015) Theory: Carlson (2003) b = - 0.560, Strinati (2004) b = - 0.545 Compare with neutron matter: a = –18 fm, R = 2 fm

2 stages of laser cooling 1. Cooling in a magneto-optical trap Tfinal = 150 mK Phase-space density ~ 10-6 2. Cooling in an optical dipole trap Tfinal = 10 nK – 10 mK Phase-space density ≈ 1

The apparatus

1st stage of cooling: Magneto-optical trap

1st stage of cooling: Magneto-optical trap mj = –1 mj = +1 mj = 0 |g>

1st stage of cooling: Magneto-optical trap N ~ 109 T ≥ 150 mK n ~ 1011 cm-3 phase space density ~ 10-6

2nd stage of cooling: Optical dipole trap Trapping potential of a focused laser beam: Laser: P = 100 W llaser=10.6 mm Trap: U ~ 250 mK The dipole potential is nearly conservative: 1 photon absorbed per 30 min b/c llaser=10.6 mm >> llithium=0.67 mm

2nd stage of cooling: Optical dipole trap Evaporative cooling - Turn on collisions by tuning to the Feshbach resonance - Evaporate The Fermi degeneracy is achieved at the cost of loosing 2/3 of atoms. Nfinal = 103 – 105 atoms, Tfinal = 0.05 EF, T = 10 nK – 1 mK, n = 1011 – 1014 cm-3

Imaging over few microseconds Absorption imaging Laser beam l=10.6 mm CCD matrix Imaging over few microseconds

Trapping atoms in anti-nodes of a standing optical wave Laser beam l=10.6 mm Mirror V(z) z Fermions: Atoms of lithium-6 in spin-states |1> and |2>

Imaging over few microseconds Absorption imaging Laser beam l=10.6 mm Mirror CCD matrix Imaging over few microseconds

Photograph of 2D systems Each cloud is an isolated 2D system Each cloud ≈ 700 atoms per spin state Period = 5.3 mm x, mm atoms/mm2 T = 0.1 EF = 20 nK z, mm [N.Novgorod, PRL 2010]

Temperature measurement from transverse density profile Linear density, mm-1 x, mm

Temperature measurement from transverse density profile T=(0.10 ± 0.03) EF Linear density, mm-1 2D Thomas-Fermi profile:

Temperature measurement from transverse density profile Gaussian fit T=(0.10 ± 0.03) EF =20 nK Linear density, mm-1 2D Thomas-Fermi profile:

The apparatus (main vacuum chamber)

Superfluid and normal hydrodynamics of a strongly-interacting Fermi gas T < 0.1 EF Superfluidity ? Duke, Science (2002)

Superfluidity 1. Bardeen – Cooper – Schreifer hamiltonian on the far Fermi side of the Feshbach resonance 2. Bogolyubov hamiltonian on the far Bose side of the Feshbach resonance

High-temperature superfluidity in the unitary limit (a → ∞) Bardeen – Cooper – Schrieffer: Theories appropriate for strong interactions Levin et al. (Chicago): Burovsky, Prokofiev, Svistunov, Troyer (Amherst, Moscow, Zurich): The Duke group has observed signatures of phase transition in different experiments at T/EF = 0.21 – 0.27

High-temperature superfluidity in the unitary limit (a → ∞) Group of John Thomas [Duke, Science 2002] Superfluidity ? vortices Group of Wolfgang Ketterle [MIT, Nature 2005] Superfluidity !!

Breathing mode in a trapped Fermi gas Image Excitation & observation: Trap ON Trap ON again, oscillation for variable 1 ms Release time 300 mm [Duke, PRL 2004, 2005]

Breathing Mode in a Trapped Fermi Gas 840 G Strongly-interacting Gas ( kF a = -30 ) w = frequency t = damping time Fit:

Breathing mode frequency w Transverse frequencies of the trap: Trap Prediction of universal isentropic hydrodynamics (either s/fluid or normal gas with many collisions): at any T Prediction for normal collisionless gas:

Frequency w vs temperature for strongly-interacting gas (B=840 G) Collisionless gas frequency, 2.11 Tc Hydrodynamic frequency, 1.84 at all T/EF !!

Damping rate 1/t vs temperature for strongly-interacting gas (B=840 G)

Hydrodynamic oscillations. Damping vs T/EF Superfluid hydrodynamics Collisional hydrodynamics of Fermi gas In general, more collisions longer damping. Bigger superfluid fraction. Collisions are Pauli blocked b/c final states are occupied. Slower damping Oscillations damp faster !!

Damping rate 1/t vs temperature for strongly-interacting gas (B=840 G)

Black curve – modeling by kinetic equation

Damping rate 1/t vs temperature for strongly-interacting gas (B=840 G) Phase transition Phase transition

Maksim Kuplyanin, A.T., Tatyana Barmashova, Kirill Martiyanov, Vasiliy Makhalov