Christian Glattli

Quantum Tomography of single charge pulses (levitons)   

D. C. Glattli¹, P. Roulleau¹, T. Jullien¹, B. Roche¹, A. Cavanna², W. Wegscheider³, Y. Jin² 

¹ Nanoelectronics group, SPEC, CEA Saclay, 91191 Gif-sur-Yvette, France
² LPN CNRS 91460 Marcoussis, France
³ ETH Solid State Physics Laboratory, Zürich, SW    

While standard quantum tomography for photons is obtained by mixing the unknown state with a large amplitude coherent photon field, for fermions like electrons in condensed matter this approach is not applicable as by nature a fermionic field is limited to small amplitude (at most one particle per state). To date no determination of an electron wave-function has been done.

Recent proposals addressing quantum conductors suggest measuring the time dependent current of electronic wave interferometers [1] or the current noise of electronic Hanbury-Brown Twiss interferometers [2–4]. Here, despite the extreme noise sensitivity required, we present such measurements [5] for single-electrons injected in a ballistic conductor. The data enable the reconstruction of the wave-function quasi-probability, called Wigner Distribution Function (WDF). Many identical electrons are prepared in a well-controlled quantum state called leviton [6]. The levitons are obtained by applying Lorentzian voltage pulses on a contact [7]. Sent to an electron beam-splitter, a Quantum Point Contact in a 2D electron gas, they are mixed with a weak amplitude fermionic field formed by a coherent superposition of electron-hole pairs generated by a small a.c. current of frequency multiple of the repetition frequency following the protocol proposed in Ref.[3]. Their anti-bunching with levitons at the beam-splitter changes the leviton partition statistics and the noise variations provide the energy density matrix elements of the levitons. The demonstration of quantum tomography makes the recent field of electron quantum optics with ballistic conductors a new test-bed for quantum information.

References
[1] Haack, G., Moskalets, M., and Büttiker, M., Phys. Rev. B 87, 201302(R) (2013).
[2] Samuelsson, P. & Büttiker, M., Phys. Rev. B 73, 041305(R) (2006).
[3] Grenier, C. et al. , New Journal of Physics 13, 093007 (2011)
[4] Ferraro, D. et al., Phys. Rev. B 88, 205303 (2013)
[5] Jullien, T., Roulleau, R., Roche, B., Cavanna, A., Jin, Y., and Glattli, D. C., Nature 514, 603-607 (2014).
[6] Dubois, J., Jullien, T., portier, F., Roche, P., Cavanna, A., Jin, Y., Wegscheider, W. and Glattli, D. C., Nature 502, 659-663 (2013)
[7] Levitov, L. S., Lee, H. & Lesovik, G. J. Math. Phys. 37, 4845–4856 (1996) ; Keeling, J., Klich, I. & Levitov, L., Phys. Rev. Lett. 97, 116403 (2006); Lebedev, A. V., Lesovik, G. V. & Blatter, G, Phys. Rev. B 72, 245314 (2005)