ABSTRACT Ultracold atoms confined by engineered magnetic or optical potentials are ideal to study phenomena otherwise difficult to realize or probe in the solid state, thanks to the ability

to control the atomic interaction strength, number of species, density and geometry. Here, we review quantum transport phenomena in atomic gases that mirror and can either better elucidate

or show fundamental differences with respect to those observed in mesoscopic and nanoscopic systems. We discuss the significant progress in transport experiments in atomic gases, the

similarities and differences between transport in cold atoms and in condensed matter systems, and survey theoretical predictions that are difficult to verify in conventional set-ups. Access

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SIMILAR CONTENT BEING VIEWED BY OTHERS ULTRACOLD CHEMISTRY AS A TESTBED FOR FEW-BODY PHYSICS Article 16 May 2024 PARAMETRIC TUNING OF QUANTUM PHASE TRANSITIONS IN ULTRACOLD REACTIONS Article

Open access 26 November 2024 QUANTUM MIXTURES OF ULTRACOLD GASES OF NEUTRAL ATOMS Article 06 November 2024 REFERENCES * Pethick, C. J. & Smith, H. _Bose–Einstein Condensation in Dilute

Gases_ 2nd edn (Cambridge Univ. Press, 2008). Book  Google Scholar  * Jaksch, D. & Zoller, P. The cold atom Hubbard toolbox. _Ann. Phys._ 315, 52–79 (2005). Article  ADS  MATH  Google

Scholar  * Lewenstein, M. et al. Ultracold atomic gases in optical lattices: Mimicking condensed matter physics and beyond. _Adv. Phys._ 56, 243–379 (2007). Article  ADS  Google Scholar  *

Cirac, J. I. & Zoller, P. Goals and opportunities in quantum simulation. _Nature Phys._ 8, 264–266 (2012). Article  ADS  Google Scholar  * Bloch, I., Dalibard, J. & Nascimbene, S.

Quantum simulations with ultracold quantum gases. _Nature Phys._ 8, 267–276 (2012). Article  ADS  Google Scholar  * Strohmaier, N. et al. Interaction-controlled transport of an ultracold

Fermi gas. _Phys. Rev. Lett._ 99, 220601 (2007). Article  ADS  Google Scholar  * Schneider, U. et al. Fermionic transport and out-of-equilibrium dynamics in a homogeneous Hubbard model with

ultracold atoms. _Nature Phys._ 8, 213–218 (2012). Article  ADS  Google Scholar  * Eckel, S. et al. Hysteresis in a quantized superfluid “atomtronic” circuit. _Nature_ 506, 200–203 (2014).

Article  ADS  Google Scholar  * Salger, T. et al. Directed transport of atoms in a Hamiltonian quantum ratchet. _Science_ 326, 1241–1243 (2009). Article  ADS  Google Scholar  * Brantut, J. 

P., Meineke, J., Stadler, D., Krinner, S. & Esslinger, T. Conduction of ultracold fermions through a mesoscopic channel. _Science_ 337, 1069–1071 (2012). Article  ADS  Google Scholar  *

Krinner, S., Stadler, D., Husmann, D., Brantut, J. P. & Esslinger, T. Observation of quantized conductance in neutral matter. _Nature_ 517, 64–67 (2015). Article  ADS  Google Scholar  *

Sommer, A., Ku, M., Roati, G. & Zwierlein, M. W. Universal spin transport in a strongly interacting Fermi gas. _Nature_ 472, 201–204 (2011). Article  ADS  Google Scholar  * Brantut, J. 

P. et al. A thermoelectric heat engine with ultracold atoms. _Science_ 342, 713–715 (2013). Article  ADS  Google Scholar  * Cheneau, M. et al. Light-cone-like spreading of correlations in a

quantum many-body system. _Nature_ 481, 484–487 (2012). Article  ADS  Google Scholar  * Krinner, S., Stadler, D., Meineke, J., Brantut, J. P. & Esslinger, T. Superfluidity with disorder

in a thin film of quantum gas. _Phys. Rev. Lett._ 110, 100601 (2013). Article  ADS  Google Scholar  * Stadler, D., Krinner, S., Meineke, J., Brantut, J. P. & Esslinger, T. Observing the

drop of resistance in the flow of a superfluid Fermi gas. _Nature_ 491, 736–739 (2012). Article  ADS  Google Scholar  * Atala, M. et al. Observation of chiral currents with ultracold atoms

in bosonic ladders. _Nature Phys._ 10, 588–593 (2014). Article  ADS  Google Scholar  * Ben Dahan, M., Peik, E., Reichel, J., Castin, Y. & Salomon, C. Bloch oscillations of atoms in an

optical potential. _Phys. Rev. Lett._ 76, 4508–4511 (1996). Article  ADS  Google Scholar  * Poli, N. et al. Precision measurement of gravity with cold atoms in an optical lattice and

comparison with a classical gravimeter. _Phys. Rev. Lett._ 106, 038501 (2011). Article  ADS  Google Scholar  * Morsch, O. & Oberthaler, M. Dynamics of Bose-Einstein condensates in

optical lattices. _Rev. Mod. Phys._ 78, 179–215 (2006). Article  ADS  Google Scholar  * Di Ventra, M. _Electrical Transport in Nanoscale Systems_ (Cambridge Univ. Press, 2008). Book  Google

Scholar  * Lee, J. G., McIlvain, B. J., Lobb, C. J. & Hill, W. T. III Analogs of basic electronic circuit elements in a free-space atom chip. _Sci. Rep._ 3, 1034 (2013). Article  ADS 

Google Scholar  * van Wees, B. J. et al. Quantized conductance of point contacts in a two-dimensional electron gas. _Phys. Rev. Lett._ 60, 848–850 (1988). Article  ADS  Google Scholar  *

Chien, C. C., Di Ventra, M. & Zwolak, M. Landauer, Kubo, and microcanonical approaches to quantum transport and noise: A comparison and implications for cold-atom dynamics. _Phys. Rev.

A_ 90, 023624 (2014). Article  ADS  Google Scholar  * Desbuquois, R. et al. Superfluid behaviour of a two-dimensional Bose gas. _Nature Phys._ 8, 645–648 (2012). Article  ADS  Google Scholar

  * Rye, C. et al. Observation of persistent flow of a Bose–Einstein condensate in a toroidal trap. _Phys. Rev. Lett._ 99, 260401 (2007). Article  ADS  Google Scholar  * Wright, K. C.,

Blakestad, R. B., Lobb, C. J., Phillips, W. D. & Campbell, G. K. Driving phase slips in a superfluid atom circuit with a rotating weak link. _Phys. Rev. Lett._ 110, 025302 (2013).

Article  ADS  Google Scholar  * Beattie, S., Moulder, S., Fletcher, R. J. & Hadzibabic, Z. Persistent currents in spinor condensates. _Phys. Rev. Lett._ 110, 025301 (2013). Article  ADS

  Google Scholar  * Albiez, M. et al. Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction. _Phys. Rev. Lett._ 95, 010402 (2005). Article  ADS 

Google Scholar  * Levy, S., Lahoud, E., Shomroni, I. & Steinhauer, J. The a.c. and d.c. Josephson effects in a Bose-Einstein condensate. _Nature_ 449, 579–583 (2007). Article  ADS 

Google Scholar  * Eckel, S., Jendrzejewski, F., Kumar, A., Lobb, C. J. & Campbell, G. K. Interferometric measurement of the current–phase relationship of a superfluid weak link. _Phys.

Rev. X_ 4, 031052 (2014). Google Scholar  * Ryu, C., Blackburn, P. W., Blinova, A. A. & Boshier, M. G. Experimental realization of Josephson junctions for an atom SQUID. _Phys. Rev.

Lett._ 111, 205301 (2013). Article  ADS  Google Scholar  * Weitenberg, C. et al. Single-spin addressing in an atomic Mott insulator. _Nature_ 471, 319–324 (2011). Article  ADS  Google

Scholar  * Celi, A. et al. Synthetic gauge fields in synthetic dimensions. _Phys. Rev. Lett._ 112, 043001 (2014). Article  ADS  Google Scholar  * Lin, Y. J. et al. Bose–Einstein condensate

in a uniform light-induced vector potential. _Phys. Rev. Lett._ 102, 130401 (2009). Article  ADS  Google Scholar  * Lin, Y. J., Compton, R. L., Jimenez-Garcia, K., Porto, J. V. &

Spielman, I. B. Synthetic magnetic fields for ultracold neutral atoms. _Nature_ 462, 628–632 (2009). Article  ADS  Google Scholar  * Goldman, N., Juzeliunas, G., Ohberg, P. & Spielman,

I. B. Light-induced gauge fields for ultracold atoms. _Rep. Prog. Phys._ 77, 126401 (2014). Article  ADS  Google Scholar  * Galitski, V. & Spielman, I. B. Spin orbit coupling in quantum

gases. _Nature_ 494, 49–54 (2013). Article  ADS  Google Scholar  * LeBlanc, L. J. et al. Observation of a superfluid Hall effect. _Proc. Natl Acad. Sci. USA_ 109, 10811–10814 (2012). Article

  ADS  Google Scholar  * Beeler, M. C. et al. The spin Hall effect in a quantum gas. _Nature_ 498, 201–204 (2013). Article  ADS  Google Scholar  * Jiménez-Garcia, K. et al. Peierls

substitution in an engineered lattice potential. _Phys. Rev. Lett._ 108, 225303 (2012). Article  ADS  Google Scholar  * Struck, J. Tunable gauge potential for neutral and spinless particles

in driven optical lattices. _Phys. Rev. Lett._ 108, 225304 (2012). Article  ADS  Google Scholar  * Jotzu, G. et al. Experimental realization of the topological Haldane model with ultracold

fermions. _Nature_ 515, 237–240 (2014). Article  ADS  Google Scholar  * Aidelsburger, M. et al. Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices. _Phys.

Rev. Lett._ 111, 185301 (2013). Article  ADS  Google Scholar  * Miyake, H., Siviloglou, G. A., Kennedy, C. J., Burton, W. C. & Ketterle, W. Realizing the Harper Hamiltonian with

laser-assisted tunneling in optical lattices. _Phys. Rev. Lett._ 111, 185302 (2013). Article  ADS  Google Scholar  * Aidelsburger, M. et al. Measuring the Chern number of Hofstadter bands

with ultracold bosonic atoms. _Nature Phys._ 11, 162–166 (2015). Article  ADS  Google Scholar  * Goldman, N. et al. Direct imaging of topological edge states in cold-atom systems. _Proc.

Natl Acad. Sci. USA_ 110, 6736–6741 (2013). Article  ADS  Google Scholar  * Peotta, S., Chien, C. C. & Di Ventra, M. Phase-induced transport in atomic gases: From superfluid to Mott

insulator. _Phys. Rev. A_ 90, 053615 (2014). Article  ADS  Google Scholar  * Nakajima, T. et al. Topological Thouless pumping of ultracold fermions. Preprint at:

http://arXiv.org/abs/1507.02223 (2015). * Lohse, M., Scweizer, C., Zilberberg, O., Aidelsburger, M. & Bloch, I. A Thouless quantum pump with ultracold bosonic atoms in an optical

superlattice. Preprint at: http://arXiv.org/abs/1507.02225 (2015). * Cao, C. et al. Universal quantum viscosity in a unitary Fermi gas. _Science_ 331, 58–61 (2011). Article  ADS  Google

Scholar  * Bardon, A. B. et al. Transverse demagnetization dynamics of a unitary Fermi gas. _Science_ 344, 722–724 (2014). Article  ADS  Google Scholar  * Ronzheimer, J. P. et al. Expansion

dynamics of interacting bosons in homogeneous lattices in one and two dimensions. _Phys. Rev. Lett._ 110, 205301 (2013). Article  ADS  Google Scholar  * Hung, C. L., Zhang, X., Gemelke, N.

& Chin, C. Slow mass transport and statistical evolution of an atomic gas across the superfluid Mott-insulator transition. _Phys. Rev. Lett._ 104, 160403 (2010). Article  ADS  Google

Scholar  * McKay, D. C., Meldgin, C., Chen, D. & DeMarco, B. Slow thermalization between a lattice and free Bose gas. _Phys. Rev. Lett._ 111, 063002 (2013). Article  ADS  Google Scholar

  * Billy, J. et al. Direct observation of Anderson localization of matter waves in a controlled disorder. _Nature_ 453, 891–894 (2008). Article  ADS  Google Scholar  * Roati, G. et al.

Anderson localization of a non-interacting Bose–Einstein condensate. _Nature_ 453, 895–898 (2008). Article  ADS  Google Scholar  * Kondov, S. S., McGehee, W. R., Zirbel, J. J. & DeMarco,

B. Three-dimensional Anderson localization of ultracold matter. _Science_ 334, 66–68 (2011). Article  ADS  Google Scholar  * Sanchez-Palencia, L. & Lewenstein, M. Disordered quantum

gases under control. _Nature Phys._ 6, 87–95 (2010). Article  ADS  Google Scholar  * Ott, H. et al. Collisionally induced transport in periodic potentials. _Phys. Rev. Lett._ 92, 160601

(2004). Article  ADS  Google Scholar  * Labouvie, R., Santra, B., Heun, S., Wimberger, S. & Ott, H. Negative differential conductivity in an interacting quantum gas. _Phys. Rev. Lett._

115, 050601 (2015). Article  ADS  Google Scholar  * Chien, C. C., Gruss, D., Di Ventra, M. & Zwolak, M. Interaction-induced conducting non-conducting transition of ultra-cold atoms in

one-dimensional optical lattices. _New J. Phys._ 15, 063026 (2013). Article  ADS  Google Scholar  * Fallani, L., Lye, J. E., Guarrera, V., Fort, C. & Inguscio, M. Ultracold atoms in a

disordered crystal of light: Towards a Bose glass. _Phys. Rev. Lett._ 98, 130404 (2007). Article  ADS  Google Scholar  * Schreiber, M. et al. Observation of many-body localization of

interacting fermions in a quasirandom optical lattice. _Science_ 349, 842–845 (2015). Article  ADS  MathSciNet  MATH  Google Scholar  * Stenger, J. et al. Bragg spectroscopy of a

Bose–Einstein condensate. _Phys. Rev. Lett._ 82, 4569–4573 (1999). Article  ADS  Google Scholar  * Seaman, B. T., Krämer, M., Anderson, D. Z. & Holland, M. J. Atomtronics: Ultracold-atom

analogs of electronic devices. _Phys. Rev. A_ 75, 023615 (2007). Article  ADS  Google Scholar  * Jeong, H., Chang, A. M. & Melloch, M. R. The Kondo effect in an artificial quantum dot

molecule. _Science_ 293, 2221–2223 (2001). Article  ADS  Google Scholar  * Törmä, P. & Sengstock, K. (eds) _Quantum Gases Experiments—Exploring Many-Body States_ (Imperial College Press,

2015). Google Scholar  * Ho, T. L. & Zhou, Q. Intrinsic heating and cooling in adiabatic processes for bosons in optical lattices. _Phys. Rev. Lett._ 99, 120404 (2007). Article  ADS 

Google Scholar  * Chien, C. C. & Di Ventra, M. Dynamical crossover between the infinite-volume and empty-lattice limits of ultra-cold fermions in 1D optical lattices. _Europhys. Lett._

99, 40003 (2012). Article  ADS  Google Scholar  * Ashcroft, N. W. & Mermin, N. D. _Solid State Physics_ (Thomson Learning, 1976). MATH  Google Scholar  Download references

ACKNOWLEDGEMENTS S.P. and M.D.V. acknowledge support from the DOE under Grant No. DE-FG02-05ER46204. S.P. acknowledges support from the Academy of Finland through its Centres of Excellence

Programme (2012–2017) under Project No. 251748. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * School of Natural Sciences, University of California, Merced, California 95343, USA Chih-Chun

Chien * Department of Physics, University of California, San Diego, California 92093, USA Sebastiano Peotta & Massimiliano Di Ventra * Department of Applied Physics, COMP Center of

Excellence, Aalto University School of Science, FI-00076 Aalto, Finland Sebastiano Peotta Authors * Chih-Chun Chien View author publications You can also search for this author inPubMed 

Google Scholar * Sebastiano Peotta View author publications You can also search for this author inPubMed Google Scholar * Massimiliano Di Ventra View author publications You can also search

for this author inPubMed Google Scholar CORRESPONDING AUTHOR Correspondence to Chih-Chun Chien. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing financial interests.

RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Chien, CC., Peotta, S. & Di Ventra, M. Quantum transport in ultracold atoms. _Nature Phys_ 11,

998–1004 (2015). https://doi.org/10.1038/nphys3531 Download citation * Received: 08 April 2015 * Accepted: 25 September 2015 * Published: 01 December 2015 * Issue Date: December 2015 * DOI:

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