Probing Cooper pairs with Franson interferometry

Giovannetti, Vittorio; Yuasa, Kazuya

doi:10.1103/physrevb.86.115429

Cited by 6 publications

(5 citation statements)

References 57 publications

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“…These contributions may prove useful in the study of entangled Cooper pairs in the wake of recent proposals to extract them from superconducting tips via field emission into vacuum. 31,32 Additionally, the results presented here allow one to make general statements about the scaling laws obeyed by these quantities in BCS and BCSlike states and provide a practical means of quantifying arXiv:1405.2184v2 [quant-ph] 14 Oct 2014 entanglement by measuring ground state fluctuations. 33 Furthermore, we demonstrate that an analysis of the entanglement spectrum of these ground states yields information on the critical properties of the model at finite temperature.…”

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confidence: 92%

Entanglement spectrum and number fluctuations in the spin-partitioned BCS ground state

2014

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We study entanglement between the spin components of the Bardeen-Cooper-Schrieffer (BCS) ground state by calculating the full entanglement spectrum and the corresponding von Neumann entanglement entropy. The entanglement spectrum is effectively modeled by a generalized Gibbs ensemble (GGE) of non-interacting electrons, which may be approximated by a canonical ensemble at the BCS critical temperature. We further demonstrate that the entanglement entropy is jointly proportional to the pairing energy and to the number of electrons about the Fermi surface (an area law). Furthermore, the entanglement entropy is also proportional to the number fluctuations of either spin component in the BCS state.PACS numbers: 74.20.Fg, 03.65.Ud Bipartite entanglement in a pure state, say ρ AB = |ψ ψ|, arises from quantum correlations between subsystem partitions A and B. Due to these correlations measurements performed on one partition, say A, exhibits fluctuations of purely quantum character. Complete information on these subsystem fluctuations is contained in the reduced density operator ρ A = tr B ρ AB , which is obtained by averaging over a complete set of states belonging to B. Quantifying entanglement in ρ AB involves measuring the degree of uncertainty of the underlying probability distribution over projections onto the Schmidt states of ρ A (that is, the eigenvalues and eigenvectors of the reduced density operator). A popular scalar measure used for this purpose is the von Neumann entanglement entropywhich is identical to the Gibbs entropy associated with the probability distribution {p i } = spec ρ A . Alternatively, the full eigenvalue spectrum of ρ A may be used as a measure of entanglement in pure states, because comparisons with effective thermal distributions can sometimes provide additional physical insight. 1-3Many recent studies of entanglement entropy in manyparticle systems focus on correlations between spatial partitions.4 This emphasis may be based on some current designs of quantum computers that manipulate entangled qubits that are separated in space. 5,6 However, the more general idea of entanglement as a manifestation of quantum correlations makes studies of entanglement under other partitioning schemes valuable in the understanding of interacting systems. For instance, a general scheme for the computation of modewise entanglement entropy that is relevant to the system discussed here has been derived for bosonic 7-10 and fermionic 11,12 Gaussian states. One of the main conclusions in these papers is that the analysis of mode entanglement in such Gaussian states can be reduced to an analysis of two-mode (pair-wise) entanglement, which greatly simplifies the theoretical study of entanglement in these many-body systems. Also, mode entanglement has been studied previously in the context of examining single-particle nonlocal quantum effects (Bell inequalities)13-17 and extractable entanglement from assemblies of identical particles for quantum information processing tasks (entanglement of particles). 18-23In t...

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confidence: 92%

Entanglement spectrum and number fluctuations in the spin-partitioned BCS ground state

2014

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“…Cooper pair splitter devices were extensively studied both experimentally [1][2][3][4][5][6][7] and theoretically [8][9][10][11][12][13][14][15][16][17][18] in recent years. They are proposed to serve as the source of spatially separated entangled electron pairs.…”

Section: Introductionmentioning

confidence: 99%

“…Theoretically, several ways were proposed to test the performance of a Cooper pair splitter device, starting from current or noise correlations, [19][20][21] through spin selective measurements [22][23][24][25] to proving the entanglement by demonstrating the violation of the Bellinequality 18,[26][27][28][29][30][31][32] or using more complex spin-qubit or circuit quantum electrodynamics architectures 17,33,34 or even time domain measurements. 35 The experiments primarily focused on spatial current correlations.…”

Section: Introductionmentioning

confidence: 99%

From Cooper pair splitting to the non-local spectroscopy of a Shiba state

Scherübl,

Fülöp,

Gramich

et al. 2021

Preprint

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Cooper pair splitting (CPS) is a way to create spatially separated, entangled electron pairs. To this day, CPS is often identified in experiments as a spatial current correlation. However, such correlations can arise even in the absence of CPS, when a quantum dot is strongly coupled to the superconductor, and a subgap Shiba state is formed. Here, we present a detailed experimental characterization of those spatial current correlations, as the tunnel barrier strength between the quantum dot and the neighboring normal electrode is tuned. The correlation of the non-local signal and the barrier strength reveals a competition between CPS and the non-local probing of the Shiba state. We describe our experiment with a simple transport model, and obtain the tunnel couplings of our device by fitting the model's prediction to the measured conductance correlation curve. Furthermore, we use our theory to extract the contribution of CPS to the non-local signal.

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“…In this perspective, we show how to define the intrinsic two-electron coherence emitted by an electron source and discuss how it encodes the information on two-electron wavefunctions. We then propose to access it through current correlations in a Franson interferometer [37] which has also been proposed to study Cooper pair coherence [38]. This naturally extends single electron coherence measurement through average current in Mach-Zehnder interferometry [39].…”

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confidence: 99%

Two-electron coherence and its measurement in electron quantum optics

et al. 2016

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Engineering and studying few-electron states in ballistic conductors is a key step towards understanding entanglement in quantum electronic systems. In this Letter, we introduce the intrinsic two-electron coherence of an electronic source in quantum Hall edge channels and relate it to two-electron wavefunctions and to current noise in an Hanbury Brown--Twiss interferometer. Inspired by the analogy with photon quantum optics, we propose to measure the intrinsic two-electron coherence of a source using low-frequency current correlation measurements at the output of a Franson interferometer. To illustrate this protocol, we discuss how it can distinguish between a time-bin entangled pure state and a statistical mixture of time shifted electron pairs.Comment: 6 pages, 6 figures, version 2 with improved introduction and bibliograph

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Probing Cooper pairs with Franson interferometry

Cited by 6 publications

References 57 publications

Entanglement spectrum and number fluctuations in the spin-partitioned BCS ground state

Entanglement spectrum and number fluctuations in the spin-partitioned BCS ground state

From Cooper pair splitting to the non-local spectroscopy of a Shiba state

Two-electron coherence and its measurement in electron quantum optics

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