Superfluid Atom Circuits

Transcription

1 Superfluid Atom Circuits Gretchen Campbell Joint Quantum Institute, NIST, University of Maryland Mid-Atlantic Senior Physicists Group June 21, 2017

2 A History of Low-Temperature Physics 1911 Superconductivity Onnes 1912 Persistent current in superconductors

3 Atomic physics biased A History of Low-Temperature Physics 1911 Superconductivity Onnes 1912 Persistent current in superconductors

4 Atomic physics biased A History of Low-Temperature Physics 1911 Superconductivity 1912 Persistent current in superconductors Onnes 1924 Theory of Bose-Einstein condensation 1938 Superfluid liquid 4 He Kapitsa Allen Landau 1938 Superfluidity related to Bose condensation Kapitza P, Nature 141, 3558 (1938) 4 He Phase Diagram

5 Atomic physics biased A History of Low-Temperature Physics 1911 Superconductivity 1912 Persistent current in superconductors Onnes 1924 Theory of Bose-Einstein condensation 1938 Superfluid liquid 4 He Kapitsa Allen Landau 1938 Superfluidity related to Bose condensation 1941 Landau critical velocity 1946 Bogoliubov Excitation Spectrum 1949 Quantized vortices (Onsager) Onsager Feynman Josephson 1962 Josephson effect in coupled superconductors

6 Atomic physics biased A History of Low-Temperature Physics 1911 Superconductivity 1912 Persistent current in superconductors Onnes 1924 Theory of Bose-Einstein condensation 1938 Superfluid liquid 4 He 1938 Superfluidity related to Bose condensation Kapitsa Allen Landau 1941 Landau critical velocity 1946 Bogoliubov Excitation Spectrum 1949 Quantized vortices (Onsager, Feynman) Onsager Feynman Josephson 1962 Josephson effect in coupled Chu Cohen-Tannoudji Phillips superconductors 1988 Laser cooling and trapping of neutral atoms 1995 Bose-Einstein condensate of ultra-cold atoms

7 What is a Quantum Fluid? Superconductors Large number of interacting particles occupying the same quantum state macroscopic wave function ψ = ψ e iφ Liquid Helium Density 2 r = y Velocity v s = m φ Neutron Stars Chemical potential µ = φ t Atomic Gases

8 Superfluid Phenomena Landau Two Fluid model Two interpenetrating fluids: Normal fluid: p n, v n Superfluid r s, v s Superfluid has zero viscosity up to a critical velocity Landau Criterion: An excitation can be created only if the flow velocity exceeds the speed of sound v c = critical velocity c = speed of sound

9 Superfluid Phenomena Zero viscosity up to a critical velocity Quantized Circulation / Persistent Currents bucket of superfluid y = y e ij! v = Ñj m ò Ñj dl = 2pn C integer winding number Simply-connected geometry Multiply-connected geometry v(r) = 0

10 Superfluid Phenomena Zero viscosity up to a critical velocity Quantized Circulation / Persistent Currents y = y e v ij ò Ñj dl = 2pn! integer C winding number = m Ñj C bucket of superfluid Current v(r) = mr ˆφ Vortex Lattice in Atomic BEC Vortices trapped in center of ring!

11 Josephson Effect Phase change across weak link g = j 2 -j 1 y ij 1 1 e e y ij 2 2 Supercurrent through weak link I = I c sin( g )

12 Atomic Bose-Einstein Condensates First Atomic BEC Temperatures: T c ~100nK Condensate size: Density: /cm 3 Weakly Interacting: Chemical potential µ ρa S Sound speed c = µ / m μ = chemical potential ρ = condensate density a s = s-wave scattering length, i.e strength of interactions C. Raman et al. PRL 83, 2502 (1999). J. Abo-Shaeer et al, Science 292, 476 (2001)

13 Atomic Bose-Einstein Condensates Sodium Atomic Beam Source Ultra-High Vacuum Cell ( P = atm.) Liquid Sodium Metal (500 K) Laser-Cooled Sodium Atoms ( 100 µk) Transferred to Optical or Magnetic traps for cooling to T c

14 Optical Dipole Force 1 F = a( wl) ÑE 2 2 Below Resonance: α > 0 Attracted to high intensity Above Resonance: α < 0 Repelled from high intensity All hyperfine states can be trapped

15 BEC and topology? Interesting effects in toroidal traps: BEC ~40 in toroidal µm trap Reduced dimensionality or topological constraints can give rise to different collective phenomena such as: Superfluidity Superflow

16 BEC and topology? Interesting effects in toroidal traps: BEC ~40 in toroidal µm trap BEC in toroidal trap with barrier Reduced dimensionality or topological constraints can give rise to different collective phenomena such as: Superfluidity Superflow Atomtronic circuits SQUID analog (Josephson junction) Interferometry/Sensors

17 BEC and topology? Interesting effects in toroidal traps: BEC ~40 in toroidal µm trap BEC in toroidal trap with barrier Reduced dimensionality or topological constraints can give rise to different collective phenomena such as: Superfluidity Superflow Atomtronic circuits SQUID analog (Josephson junction) Interferometry/Sensors

18 Superfluid(-conducting) circuits superconducting circuits SQUID Magnetometer Amplifiers Qubits J. Eom et al. Nature Phys (2012) uperfluid circuits 4 He gyroscope Majer et al. Nature (2007) build atomic superfluid circuits Simmonds et al. Nature (2001) Related work:los Alamos ETHZ,

19 JQI all-optical toroidal trap for BEC Ring beam Sheet beam Uniform to: < 0.5% of typical depth < 10% of typical µ µ = chemical potential Other Ring expts: Los Alamos (Boshier) Cambridge (Hadzibabic) Berkeley (Stamper-Kurn) U. Arizona (Anderson) Oxford (Foot) Strathclyde (Riis) 3D?D Quasi-2D ~40 µm

20 Absorption Imaging In-Situ Time-of-Flight (TOF) Spatial Information Momentum Information 0 ms 2 ms 4 ms 6 ms 8 ms 10 ms 12 ms

21 Creating Persistent Currents Blue-detuned laser creates a region of lower density 8 μm Increasing Laser Power

22 Creating Persistent Currents CirculationQuanta: v 0 = 0.15 mm/s Ω 0 = 1.2 Hz Bulk Sound Speed: c = 3-5 mm/s Ω s = Hz τ s = 50 ms

23 Readout of the persistent current: Time of Flight (Images taken after 10 ms expansion) No circulation With circulation Circulation is robust for > 1 min Limited by: Vacuum (~60 sec. BEC lifetime) Trap nonuniformity ( <5 nk)

24 Quantized Current n=0 n=1 n=2 n=3 n=4 n=0 n=1 n=2 n=3 ò Ñj dl = 2pn C

25 Readout of the persistent current: At Rest Ring BEC 20 μm Optical depth Interferometry 75 μm Concentric circles indicate no persistent current Eckel, S., et.al., Phys. Rev. X, 4, , (2014).

26 20 μm Readout of the persistent current: Rotating Ring BEC Optical depth Interferometry 1. Number of spirals arms tell you the winding number 2. Chirality tells you the direction that the current was flowing ` = 12 ` = 6 ` = 1 ` =3 ` =8 With a persistent current, you get spirals Eckel, S., et.al., Phys. Rev. X, 4, , (2014).

27 20 μm Readout of the persistent current: Rotating Ring BEC Optical depth Interferometry 1. Number of spirals arms tell you the winding number 2. Chirality tells you the direction that the current was flowing ` = 12 ` = 6 ` = 1 ` =3 ` =8 With a persistent current, you get spirals Eckel, S., et.al., Phys. Rev. X, 4, , (2014).

28 Superfluid Circuits How can we make an atom SQUID? g = j 2 -j 1 I = I c Tunnel Junction vs Weak Links sin( g ) l Current-Phase Relation g ( -1æ I ö I ) = sin ç + I è c ø LI h c I I c Kinetic/Hydrodynamic Inductance L º ml r 1D γ is the phase difference across the junction

29 Rotating the Weak Link v = 0 µ 0 chemical potential Barrier Height: U b

30 Rotating the Weak Link W v µ 0 chemical potential Barrier Height: U b

31 Rotating the Weak Link W Switch to the rotating frame! v µ 0 chemical potential 1 Barrier Height: U b I I c Ω/Ω 0

32 Rotating the Weak Link W At I c a phase slip occurs! v µ 0 chemical potential I I c 1 0 Barrier Height: U b n=0 n= Ω/Ω 0

33 Discrete Phase Slips Between Current States Average circulation U b 0.5 µ Each data point represents the average of many shots Ω/2π (Hz) Wright et. al PRL 110, (2013)

34 Hysteresis between quantized flow states g ( -1æ I ö I ) = sin ç + I è c ø LI h c I I c Kinetic/Hydrodynamic Inductance L ml " ρ 1D n = 0 n=1 E = 1 2 LI2 I c cos( γ) n n = 0 n=1 Ω (Hz) E hi c Ω/Ω 0 Eckel et. Al Nature 506, 200 (2013)

35 Hysteresis in atomtronic circuits Increasing barrier height Hysteresis plays in important role in Electronic circuits Memory Digital Noise filters SQUID magnetometers We expect hysteresis could be similarly important for atomtronic circuits Eckel et. Al Nature 506, 200 (2013)

36 Measuring the current-phase relationship Weak Links l g ( -1æ I ö I ) = sin ç + I è c ø LI h c I I c The Current-phase relationship determines the behavior of the atom circuit Using new Target trap we can interferometrically measure the phase around the ring Disk BEC at rest (phase reference) Rotating Ring BEC In-situ A similar trap has been used by the Dalibard group in Paris: PRL 113, (2014) Time-of-flight

37 Measuring the current-phase relationship BEC at rest Ω Stirred BEC - Interference between phase reference (disk) and flowing superfluid (ring) by free expansion of released clouds Df Eckel et. al, PRX 4, (2014)

38 Measuring the current-phase relationship BEC at rest Ω Stirred BEC Df n(θ) φ(θ) - v(θ) Eckel et. al, PRX 4, (2014) Phase around the ring Current around ring

39 Measuring the current-phase relationship 1 phase slips I bulk /I Ω/2 (Hz) Rotation Rate (Hz) Eckel et. al, PRX 4, (2014)

40 Measuring the current-phase relationship 1 I bulk /I Ω/2 (Hz) I WL (10 6 atoms/s) π π 0 π 2π γ (radians) g ( -1æ I ö I ) = sin ç + I è c ø LI h c I I c Eckel et. al, PRX 4, (2014)

41 Critical velocity At what velocity do phase slips occur? Gross-Pitaevskii Equation Models Zero temp behavior (speed of sound) vc (mm/s) n =1 0 Toy model which takes into account the effect of: 0 n = U 2 /µ 0 Magnus Force: Buoyancy Force: ω v n Fetter, Phys. Rev. 153, 285 (1967). Eckel et. Al Nature 506, 200 (2013)

42 What s missing from GPE? GPE w/ dissipation Dissipation? Thermal/quantum GPE fluctuations? Eckel, S., et.al., Nature, 506, 200, (2014). Mathey, A., et.al., PRA, 90, , (2014).

43 Hysteresis depends on temperature U µ 0 = 0.62(4) Increasing Temperature T = 195 nk T = 85 nk T = 40 nk Kumar, A., et.al., in preparation. Speed of sound (GPE)

44 Conclusions 1. We have observed superfluid hysteresis in a cold-atom circuit: Eckel, S., et.al., Nature, 506, 200, (2014). 2. Measured the current-phase relationship of our weak link: I WL (10 6 atoms/s) Eckel, S. et. al., Phys. Rev. X 4, (2014) & Mathew, R. et. al., Phys. Rev. A 92, (2015) 2π π 0 π 2π γ (radians)

45 Other experiments: 1. Observed resistive flow and the I-V characteristic 2. Measured the conductance through a channel: 3. Observed resonant sound (phonon) wave packets: 4. Used the Doppler effect with phonons to measure flow: 1. Jendrzejewski, F., Eckel, S., et. al., Phys. Rev. Lett., 113, (2014) 2. Lee, J.G., Eckel. S, et. al., arxiv: Wang, Yi-Hsieh, et. al., New J. Phys (2015) 4. Kumar, A., et. al., New J. Phys (2016)

46 Swarnav Steve Neal Monica Avinash Neil Ben Dan Atom Circuits /Na-Er mixture Team Avinash Kumar Neil Anderson Swarnav Banik Monica Gutierrez Hector Sosa Martinez (NP) Ultracold Strontium team Ben Reschovsky Neal Pisenti Hiro Miyake (NP) Ananya Sitaram (NP) Peter Elgee (NP) Alex Hesse (NP) Former Members Steve Eckel (NIST) Dan Barker (NIST) Fred Jendrzejewski (Heidelberg) Kevin C. Wright (Dartmouth College) R. Brad Blakestad (LPS) Anand Ramanathan (NASA Goddard) Collaborators Ian Spielman (JQI) Charles Clark (JQI) Mark Edwards (Georgia Southern) Chris J. Lobb (JQI) Wendell Hill (JQI) William D. Phillips (JQI)