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Observation of quantized conductance in neutral matter

Abstract

In transport experiments, the quantum nature of matter becomes directly evident when changes in conductance occur only in discrete steps1, with a size determined solely by Planck’s constant h. Observations of quantized steps in electrical conductance2,3 have provided important insights into the physics of mesoscopic systems4 and have allowed the development of quantum electronic devices5. Even though quantized conductance should not rely on the presence of electric charges, it has never been observed for neutral, massive particles6. In its most fundamental form, it 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 the observation of quantized conductance in the transport of neutral atoms driven by a chemical potential bias. The atoms are in an ultraballistic regime, where their mean free path exceeds not only the size of the transport channel, but also the size of the entire system, including the atom reservoirs. We use 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 the reservoirs7. By varying either a gate potential or the transverse confinement of the constrictions, we observe distinct plateaux in the atom conductance. The conductance in the first plateau is found to be equal to the universal conductance quantum, 1/h. We use Landauer’s formula to model our results and find good agreement for low gate potentials, with all parameters determined a priori. Our experiment lets us investigate quantum conductors with wide control not only over the channel geometry, but also over the reservoir properties, such as interaction strength, size and thermalization rate.

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Figure 1: An atomic QPC.
Figure 2: Conductance as a function of gate potential.
Figure 3: Conductance as a function of horizontal confinement.
Figure 4: Quantum wire: conductance as a function of gate potential.

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Acknowledgements

We acknowledge discussions with G. Blatter, K. Ensslin, C. Glattli, T. Giamarchi, C. Grenier and M. Lebrat, and thank C. Chin, T. Ihn, Y. Imry, and W. Zwerger for their careful reading of the manuscript and for discussions. We acknowledge financing from NCCR QSIT, the ERC Project SQMS, the FP7 project SIQS and ETHZ. J.-P.B. is supported by the Ambizione program of SNF.

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Correspondence to Jean-Philippe Brantut.

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Extended data figures and tables

Extended Data Figure 1 Distribution of timescales in the reservoirs.

The corresponding physical phenomena are indicated on the time line. The meanings of the different notations are defined in the text.

Extended Data Figure 2 Conductance as a function of gate potential for non-interacting reservoirs.

Filled magenta squares correspond to a scattering length of a = −4a0, whereas open blue circles represent a reference data set for weakly interacting reservoirs, where a = −187a0. Each data point is the mean of nine measurements, and error bars indicate one standard deviation. The black line is a theoretical prediction based on the Landauer formula of conductance, and the shaded region reflects the uncertainties in the input parameters.

Source data

Extended Data Figure 3 Illustration of the adiabaticity criterion.

Transverse energy level spacing Δωx = ΔEx /h along the tightly confined QPC direction (solid red line), and corresponding temporal change in the ground-state trapping frequency in the moving frame of the atoms as a function of position along the QPC for the three possible values of nz when q = 3 modes are populated.

Extended Data Figure 4 Conductance of the 2D region and of the QPC as a function of gate potential.

a, Conductance G2D as a function of gate potential in the absence of the QPC. The solid line is a linear fit to the data. b, Conductance GQPC of the QPC only, when considering the contact resistances of the 2D confinement as series resistors to the QPC. The data set, colour code, solid line and shaded region are the same as in Extended Data Fig. 2. Error bars are obtained by propagating the errors in G and G2D.

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Krinner, S., Stadler, D., Husmann, D. et al. Observation of quantized conductance in neutral matter. Nature 517, 64–67 (2015). https://doi.org/10.1038/nature14049

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