Quantum transport of fermions through mesoscopic structures

Welcome to the Lithium lab! Here we study the properties of low temperature gases of fermionic lithium-6. We use a two-terminal setup, consisting of two atomic reservoirs smoothly connected by a mesoscopic channel. This allows us to measure conductances of small cold atomic samples, such as two dimensional films and one-dimensional contacts, with direct analogies to quantum electronic devices.
Using a high-resolution microscope objective and a Digital Micromirror Device we generate almost arbitrary optical potentials for the lithium gas, ranging from single obstacles to optical lattices. This flexibility together with the unique tunability of interactions in lithium enables us to probe quantum cold atomic devices made of correlated matter.

Using near-resonant light to manipulate the atoms in a transport geometry

7th of July 2019

Ultracold atoms possess both external degrees of freedom which are manipulated by lasers and magnetic fields as well as internal degrees of freedom which are useful to emulate spin physics. Manipulating this internal degree of freedom can be realized magnetically, with radio-frequency fields, or optically using light which will act differentially on the internal states thanks to the vectorial light shift.
Optical manipulation of the internal state is very flexible thanks to beam shaping techniques. However, unless one uses specific atomic species with narrow transitions, this technique requires close to resonance beam which lead to detrimental heating.
In our set of companion papers, we use a tweezer beam localized inside the 1D wire connecting two reservoirs of a two-component Fermi gas and study both the effect of the internal state, realizing a spin filter, as well as the effect of dissipation on mesoscopic transport.

Quantized conductance through a spin-selective atomic point contact

In this set of experiment, the frequency of the light is tuned to be repulsive for one state and attractive for the other. Although the light is close to resonance, we are able to observe quantized plateaus of conductance after measuring for several seconds without detrimental heating. This lifts the degeneracy between the two spin states by twice the Fermi energy on a length on the order of the Fermi scale. This also gives us the possibility to detect minute variations the number of atoms in the channel, seeing the distance between the conductance plateaus being modified by a change of only two particles.

Read the preprint: ArXiv:1902.05516

Quantized conductance through a dissipative atomic point contact

To model transport between the two reservoirs through an atomic quantum point contact, we typically use the Landauer-Büttiker formalism which identifies transmission and conductance. In the case where there is a near-resonant beam inside the channel, a particle can be transmitted, reflected but also lost due to photon scattering. In this work we characterize how this loss affects transport and develop an extension of the Landauer-Büttiker formalism to include the losses. In addition, we also use this dissipation to map out the density in and around the transport region, similar to a dissipative scanning gate microscope for ultracold atoms.

Read the preprint: ArXiv:1907.06436

The quantized Hall conductance of a single atomic wire: A proposal based on synthetic dimensions

2nd of November 2018

Synthetic matter can help understand intricate systems where interactions compete with other phenomena, such as topological order. There has been a lot of effort from photonic and atomic platforms to realize such a system. Atoms, for instance, naturally interact between each other. Yet, it is difficult to make them behave in a topologically non trivial manner, for example by embedding them in a strong effective magnetic field. Standard approaches, for instance using a fast rotation of the gas or space-dependent dressing some internal degree of freedom, have not yet achieved effective magnetic fields which are high enough to produce the desired systems.
Here, we theoretically investigate an alternative way to create an effective magnetic field, considering the states of a harmonic oscillator as an extra spatial dimension. Combining this synthetic dimension with our usual transport wire and creating the appropriate coupling between the harmonic oscillator states allows to create an effective 2D quantum Hall bar in a 1D channel. What is more, detecting the Hall conductance can be realized in a straightforward way by varying the mean and the difference of the chemical potentials in each reservoir.

Read the paper: Phys. Rev. X 9, 041001 (2019)
Read the preprint: ArXiv:1811.00963

Breakdown of the Wiedemann-Franz law in a unitary Fermi gas

21 August 2018

Materials which are good electrical conductors typically also are good heat conductor (think of copper, etc.). This correlation between the two conductances is rooted in the fact that the same fermionic particle transport both heat and current, and is called the Wiedemann-Franz law.
In exotic materials with strong interactions between the electrons, this correlation can break down because the effective "quasi-particles" transporting the current are no longer behaving like fermions.
In our ultracold atom experiment, we have shown that this law is broken for a strongly correlated, superfluid state of matter. In particular, the heat conductivity can be an order of magnitude below its value predicted from the Wiedemann-Franz law.

Read the paper: PNAS 115 (34) 8563-8568 (2018)
Read the preprint: ArXiv:1803.00935

Band and correlated insulators of cold fermions in a mesoscopic lattice

29 March 2018

Electrical properties of materials are notoriously challenging to predict as they strongly depend on microscopic details. In particular, for particles with attractive interactions in a periodic potential, a competition is expected to occur between superfluidity, which is associated with a large conductance, and interferences, which turn the material into an insulator. Our experimental work, supported by simulations, reveals the remarkable outcome of this competition in one dimension, using ultracold fermions with widely tunable interactions in a quantum wire.
We create a short one-dimensional lattice structure connected to two reservoirs of ultracold lithium-6 atoms, which allows us to measure the wire's conductance. We first witness the emergence of a band-insulating phase with weak interactions by observing a conductance gap. By changing the length and height of the lattice, as well as the temperature, we can investigate the coherent character of particle transport. As interactions are tuned from weakly to strongly attractive, we discover that this insulating state persists, hinting at the presence of a Luther-Emery liquid, an original phase distinctive of the one-dimensional character of the structure.

Read the paper: Phys. Rev. X 8, 011053 (2018)
Read the preprint: ArXiv:1708.01250

Imaging transport of neutral atoms using a scanning gate microscope

7 February 2017

Scanning gate microscopy is a powerful technique to image transport, routinely applied to semiconductor devices. A repulsive "tip" above the sample depletes the carriers underneath and hence locally hinders their flow. By scanning the tip position and monitoring the subsequent variations of conductance, a spatial map of the structure is obtained.
We have implemented the technique for ultracold atoms using a tightly focused, repulsive laser beam, that is shaped and scanned over the atomic sample by a Digital Mirror Device. The size of the light "tip" is smaller than the Fermi wavelength, contrary to its solid state counterpart, making it sensitive to quantum tunnelling. We applied the technique to a single mode conductor and achieved a spatial resolution close to the transverse wave function inside the conductor. Furthermore, we validated the technique by comparing the scanning gate pictures to exact simulations for non-interacting particles. This technique is readily applied to interacting, as well as disordered systems.

Read the paper: Phys. Rev. Lett. 119 (2017)
Read the Physics Focus
Read the preprint: ArXiv:1702.02135

Mapping out spin and particle conductances in a quantum point contact

19 july 2016

At very low temperatures, the conductance of non-interacting particles through a quantum point contact (QPC) is an integer multiple of 1/h, the universal conductance quantum for neutral particles. This can be interpreted as a consequence of both Pauli's and Heisenberg's principle in a discrete number of conduction channels.
What happens when interactions are introduced? We address this question by measuring the conductance of a quantum degenerate Fermi gas of Lithium 6 through an optically shaped QPC as a function of chemical potential or confinement, in the weakly attractive to unitary superfluid regime. It is unexpectedly enhanced even before the gas is expected to turn into a superfluid, continuously rising from a plateau at 1/h for weak interactions to plateau-like features at non-universal values as high as 4/h for intermediate interactions. For strong interactions, the conductance plateaux disappear.
In addition, we are able to measure the spin conductance by addressing independently the chemical potentials of two different hyperfine species in the source and drain connected to the point contact. We observe a non-monotonic behaviour of the spin conductance as a function of atomic density around the QPC, which is consistent with the appearance of a superfluid gap. For weaker interactions in the normal phase, we measure a reduction of conductance from the conductance quantum 1/h, that can be attributed to one-dimensional scattering within the QPC between excitations of opposite spins. The observed breakdown of quantized conductance delivers further insights on the nature of the mid- to strongly attractive Fermi gas.

Read the paper: PNAS 113 (29) 8144-8149 (2016)
Read the preprint: ArXiv:1511.05961

Connecting strongly correlated superfluids by a quantum point contact

18 December 2015

Point contacts provide simple connections between macroscopic particle reservoirs. In electric circuits, strong links between metals, semiconductors or superconductors have applications for fundamental condensed-matter physics as well as quantum information processing. However for complex, strongly correlated materials, links have been largely restricted to weak tunnel junctions. Here we study resonantly interacting Fermi gases connected by a tunable, ballistic quantum point contact, finding a non-linear current-bias relation. At low temperature, our observations agree quantitatively with a theoretical model in which the current originates from multiple Andreev reflections. In a wide contact geometry, the competition between superfluidity and thermally activated transport leads to a conductance minimum. Our system offers a controllable platform for the study of mesoscopic devices based on strongly interacting matter.

Read the paper: Science 350, 6267 (2015)
Read the preprint: ArXiv:1508.00578
Read the Perspective by Wolfgang Belzig in Science

Observation of a Fragmented, Strongly Interacting Fermi Gas

22 July 2015

We study the emergence of a fragmented state in a strongly interacting Fermi gas subject to a tunable disorder. We investigate its properties using a combination of high-resolution in situ imaging and conductance measurements. The fragmented state exhibits saturated density modulations, a strongly reduced density percolation threshold, lower than the average density, and a resistance equal to that of a noninteracting Fermi gas in the same potential landscape. The transport measurements further indicate that this state is connected to the superfluid state as disorder is reduced. We propose that the fragmented state consists of unpercolated islands of bound pairs, whose binding energy is enhanced by the disorder.

Read the paper: Phys. Rev. Lett. 115, 045302 (2015)

Observation of quantized conductance in neutral matter

1 January 2015

In transport experiments the quantum nature of matter becomes directly evident when changes in conductance occur only in discrete steps, with a size determined solely by Planck's constant h. The observations of quantized steps in the electric conductance have provided important insights into the physics of mesoscopic systems and allowed for the development of quantum electronic devices. Even though quantized conductance should not rely on the presence of electric charges, it has never been observed for neutral, massive particles. In its most fundamental form, the phenomenon requires a quantum degenerate Fermi gas, a ballistic and adiabatic transport channel, and a constriction with dimensions comparable to the Fermi wavelength. Here we report on the observation of quantized conductance in the transport of neutral atoms. We employ high resolution lithography to shape light potentials that realize either a quantum point contact or a quantum wire for atoms. These constrictions are imprinted on a quasi two-dimensional ballistic channel connecting two adjustable reservoirs of quantum degenerate fermionic lithium atoms. By tuning either a gate potential or the transverse confinement of the constrictions, we observe distinct plateaus in the conductance for atoms. The conductance in the first plateau is found to be equal to 1/h, the universal conductance quantum. For low gate potentials we find good agreement between the experimental data and the Landauer formula, with all parameters determined a priori. Our experiment constitutes the cold atom version of a mesoscopic device and can be readily extended to more complex geometries and interacting quantum gases.

Read the paper: Nature volume 517, pages 64–67 (2015)
Read the preprint: arXiv:1404.6400

A thermoelectric heat engine with ultracold atoms

8 November 2013

Thermoelectric effects, such as the generation of a particle current by a temperature gradient, have their origin in a reversible coupling between heat and particle flows. These effects are fundamental probes for materials and have applications to cooling and power generation. Here we demonstrate thermoelectricity in a fermionic cold atoms channel in the ballistic and diffusive regimes, connected to two reservoirs. We show that the magnitude of the effect and the efficiency of energy conversion can be optimized by controlling the geometry or disorder strength. Our observations are in quantitative agreement with a theoretical model based on the Landauer-B\"uttiker formalism. Our device provides a controllable model-system to explore mechanisms of energy conversion and realizes a cold atom based heat engine.

Read the paper: Science 342, 6159 (2013)
Read the Perspective by Tero Heikkilä in Science
Read the preprint: arXiv:1306.5754

Superfluidity with disorder in thin film of quantum gas

6 march 2013

We investigate the properties of a strongly interacting superfluid gas of 6Li2 Feshbach molecules forming a thin film confined in a quasi-two-dimensional channel with a tunable random potential, creating a microscopic disorder. We measure the atomic current, extract the resistance of the film in a two-terminal configuration, and identify a superfluid state at low disorder strength, which evolves into a normal poorly conducting state for strong disorder. The transition takes place when the chemical potential reaches the percolation threshold of the disorder. The evolution of the conduction properties contrasts with the smooth behavior of the density and compressibility across the transition, measured in situ at equilibrium. These features suggest the emergence of a glasslike phase at strong disorder.

Read the paper: Phys. Rev. Lett. 110, 100601 (2013)
Read the preprint: arXiv:1211.7272

Observing the Drop of Resistance in the Flow of a Superfluid Fermi Gas

4 October 2012

The ability of particles to flow with very low resistance is a distinctive character of a superfluid or superconducting state and led to its discovery in the last century. While the particle flow in liquid Helium or superconducting materials is essential to identify superfluidity or superconductivity, an analogous measurement has not been performed with superfluids based on ultracold Fermi gases. Here we report on the direct measurement of the conduction properties of strongly interacting fermions, and the observation of the celebrated drop of resistance associated with the onset of superfluidity. We observe variations of the atomic current over several orders of magnitude by varying the depth of the trapping potential in a narrow channel, which connects two atomic reservoirs. We relate the intrinsic conduction properties to thermodynamic functions in a model-independent way, making use of high-resolution in-situ imaging in combination with current measurements. Our results show that, similar to solid-state systems, current and resistance measurements in quantum gases are a sensitive probe to explore many-body physics. The presented method is closely analogous to the operation of a solid-state field-effect transistor. It can be applied as a probe for optical lattices and disordered systems, and paves the way towards the modeling of complex superconducting devices.

Read the paper: Nature 491, 736-739 (2012)
Read the News and Views of Lincoln Carr and Mark Lusk in nature
Read the Nature News article
Read the preprint: arXiv:1210.1426

Conduction of ultra-cold Fermions through a Mesoscopic Channel

10 April 2012

In a mesoscopic conductor electric resistance is detected even if the device is defect-free. We engineer and study a cold-atom analog of a mesoscopic conductor. It consists of a narrow channel connecting two macroscopic reservoirs of fermions that can be switched from ballistic to diffusive. We induce a current through the channel and find ohmic conduction, even for a ballistic channel. An analysis of in-situ density distributions shows that in the ballistic case the chemical potential drop occurs at the entrance and exit of the channel, revealing the presence of contact resistance. In contrast, a diffusive channel with disorder displays a chemical potential drop spread over the whole channel. Our approach opens the way towards quantum simulation of mesoscopic devices with quantum gases.

Read the paper: Science 337, 6098 (2012)
Read the preprint: arXiv:1203.1927
Read the review of M. Bruderer and W. Belzig in Physik Journal (in German)
Read the commentary of T. Giamarchi in the Journal Club for Condensed Matter

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