Two-particle Aharonov-Bohm effect and entanglement in the electronic Hanbury Brown-Twiss setup

Interference between two indistinguishable electrons from independent sources

Very much like the ubiquitous quantum interference of a single particle with itself, quantum interference of two independent, but indistinguishable, particles is also possible. For a single particle, the interference is between the amplitudes of the particle's wavefunctions, whereas the interference between two particles is a direct result of quantum exchange statistics. Such interference is observed only in the joint probability of finding the particles in two separated detectors, after they were injected from two spatially separated and independent sources. Experimental realizations of two-particle interferometers have been proposed; in these proposals it was shown that such correlations are a direct signature of quantum entanglement between the spatial degrees of freedom of the two particles ('orbital entanglement'), even though they do not interact with each other. In optics, experiments using indistinguishable pairs of photons encountered difficulties in generating pairs of independent photons and synchronizing their arrival times; thus they have concentrated on detecting bunching of photons (bosons) by coincidence measurements. Similar experiments with electrons are rather scarce. Cross-correlation measurements between partitioned currents, emanating from one source, yielded similar information to that obtained from auto-correlation (shot noise) measurements. The proposal of ref. 3 is an electronic analogue to the historical Hanbury Brown and Twiss experiment with classical light. It is based on the electronic Mach-Zehnder interferometer that uses edge channels in the quantum Hall effect regime. Here we implement such an interferometer. We partitioned two independent and mutually incoherent electron beams into two trajectories, so that the combined four trajectories enclosed an Aharonov-Bohm flux. Although individual currents and their fluctuations (shot noise measured by auto-correlation) were found to be independent of the Aharonov-Bohm flux, the cross-correlation between current fluctuations at two opposite points across the device exhibited strong Aharonov-Bohm oscillations, suggesting orbital entanglement between the two electron beams.

An on-demand coherent single-electron source

We report on the electron analog of the single-photon gun. On-demand single-electron injection in a quantum conductor was obtained using a quantum dot connected to the conductor via a tunnel barrier. Electron emission was triggered by the application of a potential step that compensated for the dot-charging energy. Depending on the barrier transparency, the quantum emission time ranged from 0.1 to 10 nanoseconds. The single-electron source should prove useful for the use of quantum bits in ballistic conductors. Additionally, periodic sequences of single-electron emission and absorption generate a quantized alternating current.

Tunable noise cross correlations in a double quantum dot

We report measurements of the cross correlation between temporal current fluctuations in two capacitively coupled quantum dots in the Coulomb blockade regime. The sign of the cross-spectral density is found to be tunable by gate voltage and source-drain bias. We find good agreement with the data by including an interdot Coulomb interaction in a sequential-tunneling model.

Entanglement, dephasing, and phase recovery via cross-correlation measurements of electrons

Determination of the path taken by a quantum particle leads to a suppression of interference and to a classical behavior. We employ here a quantum "which path" detector to perform accurate path determination in a two-path Mach-Zehnder electron interferometer, leading to full suppression of the interference. Following the dephasing process we recover the interference by measuring the cross correlation between the interferometer and detector currents. Under our measurement conditions every interfering electron is dephased by approximately a single electron in the detector-leading to mutual entanglement of approximately single pairs of electrons.

Leggett-Garg inequality with a kicked quantum pump

A kicked quantum nondemolition measurement is introduced, where a qubit is weakly measured by pumping current. Measurement statistics are derived for weak measurements combined with single-qubit unitary operations. These results are applied to violate a generalization of the Leggett-Garg inequality. The violation is related to the failure of the noninvasive detector assumption, and may be interpreted as either intrinsic detector backaction, or the qubit entangling the microscopic detector excitations. The results are discussed in terms of a quantum point contact kicked by a pulse generator, measuring a double quantum dot.

Bidirectional Counting of Single Electrons

A bidirectional single-electron counting device is demonstrated. Individual electrons flowing in forward and reverse directions through a double quantum dot are detected with a quantum point contact acting as a charge sensor. A comprehensive statistical analysis in the frequency and time domains and of higher order moments of noise reveals antibunching correlation in single-electron transport through the device itself. The device can also be used to investigate current flow in the attoampere range, which cannot be measured by existing current meters.

Entanglement of two impurities through electron scattering

We study how two magnetic impurities embedded in a solid can be entangled by an injected electron scattering between them and by subsequent measurement of the electron's state. We start by investigating an ideal case where only the electronic spin interacts successively through the same unitary operation with the spins of the two impurities. We find conditions for the impurity spins to be maximally entangled with a significant success probability. We then consider a more realistic description which includes both the forward and backscattering amplitudes. In this scenario, we obtain the entanglement between the impurities as a function of the interaction strength of the electron-impurity coupling. We find that our scheme allows us to entangle the impurities maximally with a significant probability.

Quantum tunneling detection of two-photon and two-electron processes

We analyze the operation of a quantum tunneling detector coupled to a coherent conductor. We demonstrate that, in a certain energy range, the output of the detector is determined by two-photon processes, two-interacting-electron processes, and the interference of the two. We show how the individual contributions of these processes can be resolved in experiments.

Multiparticle interference, Greenberger-Horne-Zeilinger entanglement, and full counting statistics

We investigate the quantum transport in a generalized N-particle Hanbury Brown-Twiss setup enclosing magnetic flux, and demonstrate that the Nth-order cumulant of current cross correlations exhibits Aharonov-Bohm oscillations, while there is no such oscillation in all the lower-order cumulants. The multiparticle interference results from the orbital Greenberger-Horne-Zeilinger entanglement of N indistinguishable particles. For sufficiently strong Aharonov-Bohm oscillations the generalized Bell inequalities may be violated, proving the N-particle quantum nonlocality.

Unexpected behavior in a two-path electron interferometer

We report the observation of an unpredictable behavior of a simple, two-path, electron interferometer. Utilizing an electronic analog of the well-known optical Mach-Zehnder interferometer, with current carrying edge channels in the quantum Hall effect regime, we measured high contrast Aharonov-Bohm (AB) oscillations. Surprisingly, the amplitude of the oscillations varied with energy in a lobe fashion, namely, with distinct maxima and zeros (namely, no AB oscillations) in between. Moreover, the phase of the AB oscillations was constant throughout each lobe period but slipped abruptly by pi at each zero. The periodicity of the lobes defines a new energy scale, which may be a general characteristic of quantum coherence of interfering electrons.

Detecting entanglement using a double-quantum-dot turnstile

We propose a scheme based on using the singlet ground state of an electron spin pair in a double-quantum-dot nanostructure as a suitable setup for detecting entanglement between electron spins via the measurement of an optimal entanglement witness. Using time-dependent gate voltages and magnetic fields the entangled spins are separated and coherently rotated in the quantum dots and subsequently detected at spin-polarized quantum point contacts. We analyze the coherent time evolution of the entangled pair and show that by counting coincidences in the four exits an entanglement test can be done. This setup is close to present-day experimental possibilities and can be used to produce pairs of entangled electrons "on demand."

Counting statistics and detector properties of quantum point contacts

Quantum detector properties of the quantum point contact (QPC) are analyzed for an arbitrary electron transparency and coupling strength to the measured system and are shown to be determined by the electron counting statistics. Conditions of the quantum-limited operation of the QPC detector, which prevent information loss through the scattering time and scattering phases, are found for arbitrary coupling. We show that the phase information can be restored and used for the quantum-limited detection by inclusion of the QPC detector in the electronic Mach-Zehnder interferometer.

Optimal spin-entangled electron-hole pair pump

A nonperturbative theory is presented for the creation by an oscillating potential of spin-entangled electron-hole pairs in the Fermi sea. In the weak potential limit, considered earlier by Samuelsson and Büttiker, the entanglement production is much less than 1 bit per cycle. We demonstrate that a strong potential oscillation can produce an average of one Bell pair per two cycles, making it an efficient source of entangled flying qubits.

Mesoscopic one-way channels for quantum state transfer via the quantum Hall effect

We show that the one-way channel formalism of quantum optics has a physical realization in electronic systems. In particular, we show that magnetic edge states form unidirectional quantum channels capable of coherently transporting electronic quantum information. Using the equivalence between one-way photonic channels and magnetic edge states, we adapt a proposal for quantum state transfer to mesoscopic systems using edge states as a quantum channel, and show that it is feasible with reasonable experimental parameters. We discuss how this protocol may be used to transfer information encoded in number, charge, or spin states of quantum dots, so it may prove useful for transferring quantum information between parts of a solid-state quantum computer.