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International Congress on Mathematical Physics (ICMP)

ENTANGLEMENT AT FINITE TEMPERATURE IN THE ELECTRONIC TWO-PARTICLE INTERFEROMETER

Peter Samuelsson, Izhar Neder, Μ. Büttiker

Published Mar 1, 2010• 0 citations
Publisher

Abstract

In this work we discuss a theory for entanglement generation, characterization and detection in fermionic two-particle interferometers (2PI) at finite temperature. The motivation for our work is provided by the recent experiment by the Heiblum group, Neder et al. Nature 448, 333 (2007), realizing the 2PI proposed by Samuelsson, Sukhorukov, and Buttiker, Phys. Rev. Lett. 92, 026805 (2004). The experiment displayed a clear two-particle Aharonov-Bohm effect, however with an amplitude suppressed due to finite temperature and dephasing. In our recent work Samuelsson, Neder, and Buttiker, Phys. Rev. Lett. 102, 106804 (2009) we presented a general theory for finite temperature entanglement in mesoscopic conductors and applied it to the 2PI, here further discussed.

DOI
10.1142/9789814304634_0048

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In this work we discuss a theory for entanglement generation, characterization and detection in fermionic two-particle interferometers (2PI) at finite temperature. The motivation for our work is provided by the recent experiment by the Heiblum group, Neder et al. Nature 448, 333 (2007), realizing the 2PI proposed by Samuelsson, Sukhorukov, and Buttiker, Phys. Rev. Lett. 92, 026805 (2004). The experiment displayed a clear two-particle Aharonov-Bohm effect, however with an amplitude suppressed due to finite temperature and dephasing. In our recent work Samuelsson, Neder, and Buttiker, Phys. Rev. Lett. 102, 106804 (2009) we presented a general theory for finite temperature entanglement in mesoscopic conductors and applied it to the 2PI, here further discussed.
In this work we discuss a theory for entanglement generation, characterization and detection in fermionic two-particle interferometers (2PIs) at finite temperature. The motivation for our work is provided by the recent experiment by the Heiblum group (Neder et al 2007 Nature 448 333) realizing the two particle interferometer proposed by Samuelsson et al (2004 Phys. Rev. Lett. 92 026805). The experiment displayed a clear two-particle Aharonov–Bohm effect, however with an amplitude suppressed due to finite temperature and dephasing. This raised qualitative as well quantitative questions about entanglement production and detection in mesoscopic conductors at finite temperature. As a response to these questions, in our recent work (Samuelsson et al 2009 Phys. Rev. Lett. 102 106804), we presented a general theory for finite temperature entanglement in mesoscopic conductors. Applied to the 2PI we showed that the emitted two-particle state in the experiment was clearly entangled. Moreover, we demonstrated that the entanglement of the reduced two-particle state, reconstructed from measurements of average currents and current cross correlations, constitutes a lower bound to the entanglement of the emitted state. The present work provides an extended and more detailed discussion of these findings.
We present a theory for two-particle entanglement production and detection in mesoscopic conductors at finite temperature. The entanglement of the density matrix projected out of the emitted many-body state differs from the entanglement of the reduced density matrix, detectable by current correlation measurements. Under general conditions reduced entanglement constitutes a witness for projected entanglement. Applied to the recent experiment [Neder et al., Nature (London) 448, 333 (2007)10.1038/nature05955] on a fermionic Hanbury Brown Twiss two-particle interferometer we find that despite an appreciable entanglement production in the experiment, the detectable entanglement is close to zero.
We review recent theoretical investigations on the two-particle Aharonov–Bohm effect and its relation to entanglement production and detection. The difficulties of the entanglement detection due to dephasing and finite temperature are discussed regarding a recent experimental realization of a two-particle Aharonov–Bohm interferometer [15]. We also discuss a theoretical proposal for a two-particle Aharonov–Bohm interferometer, which as against the finite bias setup is driven with dynamical single-electron sources allowing for the tunable production of time-bin entanglement.
We analyze a Hanbury Brown-Twiss geometry in which particles are injected from two independent sources into a mesoscopic conductor in the quantum Hall regime. All partial waves end in different reservoirs without generating any single-particle interference; in particular, there is no single-particle Aharonov-Bohm effect. However, exchange effects lead to two-particle Aharonov-Bohm oscillations in the zero-frequency current cross correlations. We demonstrate that this is related to two-particle orbital entanglement, detected via violation of a Bell inequality. The transport is along edge states and only adiabatic quantum point contacts and normal reservoirs are employed.
We show that multimode entanglement of electrons in a mesoscopic conductor can be detected by a measurement of the zero-frequency current correlations in an electronic Hong-Ou-Mandel interferometer. By this means, one can further establish a lower bound to the entanglement of formation of two-electron input states. Our results extend the work of Burkard and Loss [Phys. Rev. Lett. 91, 087903 (2003)] to many channels and provide a way to test the existence of entangled states involving both orbital and spin degrees of freedom.
The entanglement of coherently split electron-hole pairs in an electronic conductor is typically not considered accessible due to particle number conservation and fermionic superselection rules. We demonstrate here that current cross-correlation measurements at the outputs of an electronic Mach-Zehnder interferometer can nevertheless provide a robust witness of electron-hole entanglement. Specifically, we consider neutral excitations generated by modulating the transmission of an unbiased quantum point contact periodically in time. For an optimized modulation profile, an entangled state with one positively-charged leviton (a hole) and one negatively-charged leviton (an electron) gets delocalized over the two paths of the interferometer and is detected at the output arms. We evaluate the influence of finite electronic temperatures and dephasing corresponding to recent experiments.