Quantum Transport in Ultracold Atoms. Chih-Chun Chien ( 簡志鈞 ) University of California, Merced

Transcription

1 Quantum Transport in Ultracold Atoms Chih-Chun Chien ( 簡志鈞 ) University of California, Merced

2 Outline Introduction to cold atoms Atomtronics simulating and complementing electronic devices using cold atoms similarities and differences Steady-state current with time-dependent density distributions Quantum memory effects in isolated noninteracting systems Negative differential conductivity in quantum systems Summary

3 Introduction To Cold Atoms Superfluid Mott insulator PRL 84, 806 (2000) Review: I. Bloch, Nat. Phys. 1, 23 (2005) Nature 472, 201 (2011) Little Fermion Collider (LFC)

4 Quantum Transport In Cold Atoms (a) Density-induced transport (Nat. Phys. 8, 213 (2012)) (b) Atomic superfluid in a ring (Nature 506, 200 (2014)) (c) Quantum ratchet (Science 326, 1241 (2009)) (d) Quantized conductance (Nature 517, 64 (2015))

5 Comparison With Electronics A. Double quantum dot (Science 293, 2221 (2001)) B. Quantum conductance (Science 342, 713 (2014)) C. Atomic RC circuit (Sci. Rep. 3, 1034 (2013)) Conventional setup: Source Gate Drain Number conservation will make a difference.

6 Comparison

7 How to Induce Currents? Electronic transport: Driven by electromagnetic field from batteries First battery, Volta Cold atoms: (1) Time-dependent trapping potentials (Science 326, 1241 (2009)); (2) Out-ofequilibrium initial states (Nature 472, 211 (2011)); (3) Artificial vector potential (PRA 87, (2013)); (4) Density or interaction imbalance ((Nature 517, 64 (2015), New J. Phys. 15, (2013)); and many other ways.

8 Landauer Formalism Consider 3 parts: L, R, and Junction (Open systems) EC VL,C VR,C L R (See Landauer, IBM J. Res. Dev. 1, 223 (1957); Jauho, Wingree,Meir, PRB 50, 5528 (1994); Di Ventra s book.) e I = de [ f L ( E) f R ( E )]T ( E) πh T ( E )=GL G G R G =GL GR G ret adv ΓL / R = 2Im[Σ ret L / R,C ] ret 2 ret G ret = 1/[E E C Σ ret Σ L,C R,C ] Σ L / R,C = VL / R,C GL / R The assumption of infinite reservoirs leads to the static Fermi-Dirac distribution for fermions.

9 Micro-Canonical Formalism Recipe: (1)Prepare the system in the ground state or equilibrium state of H 0. (2)Evolve all operators with H e idc j /dt = [c j,h e ] (3)Calculate physical quantities I = d N L /dt A small system of 60 sites and 30 particles exhibits a quasisteady state current. Bushong et al., Nano Lett. 5, 2569 (2005)

10 Number Conservation Leads To Time-Dependent Distributions 1. Load atom(s) into the left half lattice. 2. Lift the barrier. Analogy of dam break e de [ f L ( E) f R ( E )]T ( E)?? I = πh If fl decreases and fr increases, the Landauer formula suggests a decaying current.

11 Quasi-Steady State Current With Time-Dependent Distributions The emergence of a QSSC does not rely on a stationary distribution. By adding a bias, the populations can reverse while the current remains constant. Chien et. al.,pra 90, (2014)

12 Searching For Quantum Memory Effects With Chen-Yen Lai UC Merced

13 Where Can We See Memory Effects? Hysteresis Memory Foam Battery Almost everywhere, but most of them are classical.

14 Memory Effects In Atomic Superfluids Nature 506, 200 (2014). The atomic superfluid resists the stirring.

15 Memory Effect in Noninteracting Quantum Systems The current exhibits no memory effects. Chien et al., New J. Phys 15, (2013), Phy. Rev. A 87, (2013), Phys. Rev. A 90, (2014). And it seems general. (Cornean et al., Ann. Henri Poincare (2013)) A bound state can introduce competing time scales.

16 Can We Use Flat Bands Instead? Kagome Lattice Band structure: The flat band could also introduce a different time scale!

17 Optical Triangular And Kagome Lattices Stamper-Kurn's group PRL 108, (2012)

18 Steady-State After Lattice Transformation From a triangular to a kagome lattice Density re-distribution. There is no dissipation mechanism. But fermions without interactions enter a steady state. Band theory for infinite systems. To square To square To kagome To kagome Schrodinger equation for finite-size systems.

19 Memory Effect From Band Theory The remaining density on Dsites exhibits memory effects. Temperature washes out the memory effect. Phys. Rev. Applied 5, (2016)

20 Memory Effects in Finite Systems Solve Schrodinger equation using finitedifference method (at T=0). Memory effects are observable in the density of site-d. To square To kagome

21 Application Differentiator and Accelerometer Electronic differentiator: Probing acceleration and recording the rate. (Suitable for ~ms time scale.)

22 Negative Differential Conductivity Physics Today 23, 35 (1970) From Wikipedia

23 Interaction-Driven Transport Optical Feshbach resonance: PRL 77, 2913 (1996), PRL 85, 4462 (2000), PRL 93, (2004), PRL 105, (2010), PRL 107, (2011), PRL 110, (2013). Two component fermions: H = t ij c c j +U Mean-field (Hartree-Fock) theory i j L n j n j

24 Conducting-Nonconducting Transition Noninteracting fermions driven by a bias. Interaction-induced transport. Energy conservation and mismatch is the key!

25 Can We Trust Mean-Field Theory? Time-dependent density matrix renormalization group simulations qualitatively agree with the mean-field result. The conductingnonconducting transition survives. (New J. Phys. 15, (2013))

26 NDC of Interacting Bosons Interplays among the chemical potential, interaction energy, and energy-level couplings lead to negative differential conductivity. PRL 115, (2015)

27 Slow Thermalization Due To Energy Mismatch Suppression of thermalization of two-component bosons. PRL 111, (2013).

28 Summary Ultracold atoms in artificial potentials can mimic electronic systems and exhibit interesting transport behavior. The differences between cold-atoms and electronics could lead to superficial agreements despite different mechanisms. Cold-atom transport brings novel phenomena and applications, such as quantum memory effects and nonequlibrium transitions. Thank you!

29 Quantum Memory Effect Atomic Memory (QMEAM) Write-in scheme Lai and Chien, Phys. Rev. Applied 5, (2016)

30 Read-Out Scheme For Memory-Effect Devices Based on Nat Phys 4, 949 (2008). Based on Phys. Rev. A 90, (2014)

31 Ultra-Cold Atoms 101 Laser-cooled vapor trapped by optical and/or magnetic potentials. Interactions are from two-body collisions. Bosons Fermions Bose-Einstein Condensation (BEC) 1995 (Cornell, Ketterle, Pauli exclusion: Need two (or more) components to have interactions Wieman, 2001 Nobel Prize) Lower T (Cornell & Wieman) Li-7,Na-23,Rb-87,Cs-133 Stronger attraction (Jin) Li-6, K-40