arXiv subjects

Xin-Qi Li

Publications and source records attributed to Xin-Qi Li.

At least 37 records · Page 2Linked to original sources

arXiv2021

Majorana Conductances in Three-Terminal Transports

We consider a two-lead (three-terminal) setup of nonlocal transport through Majorana zero modes (MZMs) and construct a Majorana master equation (which is also valid for small bias voltage). We first carry out representative results of current and then show that a modified Bogoliubov-de Gennes (BdG) treatment can consistently recover the same results. Based on the interplay of the two approaches, we reveal the existence of nonvanishing channels of teleportation and crossed Andreev reflections even at the limit $ε_M\to 0$ (zero coupling energy of the MZMs), which leads to new predictions for the height of the zero-bias-peak of the local conductance and the $ε_M$-scaling behavior of the teleportation conductance, for verification by experiments.

cond-mat.mes-hall↗

arXiv2021

Cross correlation mediated by distant Majorana zero modes with no overlap

Existing studies via shot noise calculation conclude that the cross correlation between the currents in the two leads connected by a pair of Majorana zero modes (MZMs) vanishes when their coupling energy $ε_M\to 0$. Motivated by the intrinsic nature of nonlocality of the MZMs, we revisit this important problem and propose an experimental scheme to demonstrate the nonvanishing cross correlation even at the limit $ε_M\to 0$. The proposed scheme employs the Andreev-process-associated branch circuit currents, which are theoretically obtained by applying a decomposition analysis for the total currents while in practical measurement, are accessible directly. For different bias voltage setup, we find intriguing results of both negative and positive correlations and carry out simple physical understanding using a quantum jump technique. Importantly, combining together with the evidence of the zero-bias-peak of conductance, the nonlocal cross correlation predicted in this work can help to definitely confirm the existence of the nonlocal MZMs.

quant-ph↗

arXiv2020

Weak-value-amplification analysis beyond the AAV limit of weak measurements

The weak-value (WV) measurement proposed by Aharonov, Albert and Vaidman (AAV) has attracted a great deal of interest in connection with quantum metrology. In this work, we extend the analysis beyond the AAV limit and obtain a few main results. (i) We obtain non-perturbative result for the signal-to-noise ratio (SNR). In contrast to the AAV's prediction, we find that the SNR asymptotically gets worse when the AAV's WV $A_w$ becomes large, i.e., in the case $g|A_w|^2>>1$, where $g$ is the measurement strength. (ii) With the increase of $g$ (but also small), we find that the SNR is comparable to the result under the AAV limit, while both can reach -- actually the former can slightly exceed -- the SNR of the standard measurement. However, along a further increase of $g$, the WV technique will become less efficient than the standard measurement, despite that the postselection probability is increased. (iii) We find that the Fisher information can characterize the estimate precision qualitatively well as the SNR, yet their difference will become more prominent with the increase of $g$. (iv) We carry out analytic expressions of the SNR in the presence of technical noises and illustrate the particular advantage of the imaginary WV measurement. The non-perturbative result of the SNR manifests a favorable range of the noise strength and allows an optimal determination.

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arXiv2020

Revisit the non-locality of Majorana zero modes and teleportation: Bogoliubov-de Gennes equation based treatment

The nonlocal nature of the Majorana zero modes implies an inherent teleportation channel and unique transport signatures for Majorana identification. In this work we make an effort to eliminate some inconsistencies between the Bogoliubov-de Gennes equation based treatment and the method using the associated regular fermion number states of vacancy and occupation within the `second quantization' framework. We first consider a rather simple `quantum dot--Majorana wire--quantum dot' system, then a more experimentally relevant setup by replacing the quantum dots with transport leads. For the latter setup, based on the dynamical evolution of electron-hole excitations, we develop a single-particle-wavefunction approach to quantum transport, which renders both the conventional quantum scattering theory and the steady-state nonequilibrium Green's function formalism as its stationary limit. Further, we revisit the issue of Majorana tunneling spectroscopy and consider in particular the two-lead coupling setup. We present comprehensive discussions with detailed comparisons, and predict a zero-bias-limit conductance of $e^2/h$ (for symmetric coupling to the leads),which is a half of the popular result of the zero-bias-peak, or, the so-called Majorana quantized conductance ($2e^2/h$). The present work may arouse a need to reexamine some existing studies and the proposed treatment is expected to be involved in analyzing future experiments in this fast developing field.

cond-mat.mes-hall↗

arXiv2020

Quantum transfer through a continuum under continuous monitoring

In this work we extend our previous studies on the quantum transfer of a particle through a finite-bandwidth continuum under frequent detections, by replacing the assumed frequent measurements with a genuine continuous monitoring by a point-contact detector. We present a quantitative comparison between the two types of measurement. We also propose possible measurements, based on the state-of-the-art experiments, to test the `scaling' property between the measurement rate and the bandwidth of the reservoir, rooted in the transfer dynamics under continuous monitoring.

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arXiv2020

Double-dot interferometer for quantum measurement of Majorana qubits and stabilizers

Motivated by the need of quantum measurement of Majorana qubits and surface-code stabilizers, we analyze the performance of a double-dot interferometer under the influence of environment noise. The double-dot setup design allows accounting for the full multiple tunneling process between the dots through the Majorana island, within a master equation approach. In the co-tunneling regime, which results in a Majorana-mediated effective coupling between the dots, the master equation approach allows us to obtain analytic solutions for the measurement currents. The measurement quality, characterized by figures of merit such as the visibility of measurement signals, is carried out in regard to the unusual decoherence effect rather than `which-path' dephasing. The results obtained in this work are expected to be useful for future experiments of Majorana qubit and stabilizer measurements.

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arXiv2019

Direct measurement of the quantum state of photons in a cavity

We propose a scheme to measure the quantum state of photons in a cavity. The proposal is based on the concept of quantum weak values and applies equally well to both the solid-state circuit and atomic cavity quantum electrodynamics (QED) systems. The proposed scheme allows us to access directly the superposition components in Fock state basis, rather than the Wigner function as usual in phase space. Moreover, the separate access feature held in the direct scheme does not require a global reconstruction for the quantum state, which provides a particular advantage beyond the conventional method of quantum state tomography.

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arXiv2019

Transport Signatures of a Majorana Qubit and Read-out-induced Dephasing

Motivated by recent proposals of Majorana qubits and the read-out of their quantum state we investigate a qubit setup formed by two parallel topological wires shunted by a superconducting bridge. The wires are further coupled to two quantum dots, which are also linked directly, thus creating an interference loop. The transport current through this system shows an interference pattern which distinguishes two basis states of the qubit in a QND measurement. We analyze various properties of the interference current and the read-out process, including the resulting dephasing and relaxation. We also analyze the effects of varying control parameters such as gate voltages on the current. The characteristic dependencies could serve as a signature of Majorana bound states.

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arXiv2019

Theory for frequent measurements of spontaneous emissions in non-Markovian environment: beyond Lorentzian spectrum

The measurement-result-conditioned evolution of a system (e.g. an atom) with spontaneous emissions of photons is well described by the quantum trajectory (QT) theory. In this work we generalize the associated QT theory from infinitely wide bandwidth Markovian environment to the case of finite bandwidth non-Markovian environment. In particular, we generalize the treatment for arbitrary spectrum, which is not restricted by the specific Lorentzian case. We rigorously prove a general existence of a perfect scaling behavior jointly defined by the bandwidth of environment and the time interval between successive photon detections. For a couple of examples, we obtain analytic results to facilitate QT simulations based on the Monte-Carlo algorithm. For the case where analytical result is not available, numerical scheme is proposed for practical simulations.

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arXiv2019

Counting statistics of photon emissions detected in non-Markovian environment

In this work we present a large-deviation analysis for the counting statistics of atomic spontaneous emissions continuously detected in finite-bandwidth non-Markovian environment. We show that the statistics of the spontaneous emissions depends on the response time of the detector, which can result in big differences such as dynamical phase transition. This feature excludes the idea of regarding the spontaneous emissions as detection-free objective events. Possible experiment is briefly discussed in connection with the state-of-the-art optical cavity set-up.

quant-ph↗

arXiv2019

Gradual partial-collapse theory for ideal nondemolition measurements of qubits in circuit QED

The conventional method of qubit measurements in circuit QED is employing the dispersive regime of qubit-cavity coupling, which results in an approximated scheme of quantum nondemolition (QND) readout. This scheme becomes problematic in the case of strong coupling and/or strong measurement drive, owing to the so-called Purcell effect. A recent proposal by virtue of longitudinal coupling suggests a new scheme to realize fast, high-fidelity, and {\it ideal QND} readout of qubit state. The aim of the present work is twofold: (i) In parallel to what has been done in the past years for the dispersive readout, we carry out the gradual partial-collapse theory for this recent scheme, in terms of both the quantum trajectory equation and quantum Bayesian approaches. The partial-collapse weak measurement theory is useful for such as the measurement-based feedback control and other quantum applications. (ii) In the physical aspect, we construct the joint qubit-plus-cavity entangled state under continuous measurement and present a comprehensive analysis for the quantum efficiency,qubit-state purity, and signal-to-noise ratio in the output currents. The combination of the joint state and the quantum Bayesian rule provides a generalized scheme of cavity reset associated with the longitudinal coupling, which can restore the qubit to a quantum pure state from entanglement with the cavity states, and thus benefits the successive partial-collapse measurements after qubit rotations.

quant-ph↗

arXiv2019

Estimation of parameters in circuit QED by continuous quantum measurement

Designing high-precision and efficient schemes is of crucial importance for quantum parameter estimation in practice. The estimation scheme based on continuous quantum measurement is one possible type of this, which looks also the most natural choice in case such as continuous dynamical process. In this work we specify the study to the stat-of-the-art superconducting circuit quantum-electrodynamics (QED) system, where the high-quality continuous measurement has been extensively exploited in the past decade. Within the framework of Bayesian estimation and particularly using the quantum Bayesian rule in circuit QED, we numerically simulate the likelihood function as estimator for the Rabi frequency of qubit oscillation. We find that, by proper design of the interaction strength of measurement, the estimate precision can scale with the measurement time beyond the standard quantum limit, which is usually assumed for this type of continuous measurement since no more special quantum resource is involved. We understand this remarkable result by quantum correlation in time between the output signals, and simulate the effect of quantum efficiency of the measurement on the precision scaling behavior.

quant-ph↗

arXiv2017

Low-field electron mobility of InSb nanowires: Numerical efforts to larger cross sections

Within the framework of Boltzmann equation, we present a $\mathbf{k\cdot p}$ theory based study for the low-field mobilities of InSb nanowires (InSb NWs) with relatively large cross sectional sizes (with diameters up to 51.8 nm). For such type of large size nanowires, the intersubband electron-phonon scattering is of crucial importance to affect the scattering rate and then the mobility. In our simulation, the lowest 15 electron subbands and 50 transverse modes of phonons are carefully accounted for. We find that, up to the 51.84 nm diameter, the mobility monotonously increases with the diameter, not yet showing any saturated behavior. We also find that, while the bulk InSb mobility is considerably higher than the bulk Si, the small size (e.g. $\sim 3$ nm diameter) nanowires from both materials have similar magnitude of mobilities. This implies, importantly, that the mobility of the InSb NWs would decrease faster than the SiNWs as we reduce the cross sectional size of the nanowires.

cond-mat.mes-hall↗

arXiv2016

Majorana dc Josephson current mediated by a quantum dot

The Josephson supercurrent through the hybrid Majorana--quantum dot--Majorana junction is investigated. We particularly analyze the effect of spin-selective coupling between the Majorana and quantum dot states, which emerges only in the topological phase and will influence the current through bent junctions and/or in the presence of magnetic fields in the quantum dot. We find that the characteristic behaviors of the supercurrent through this system are quite counterintuitive, remarkably differing from the resonant tunneling, e.g., through the similar (normal phase) superconductor--quantum dot--superconductor junction. Our analysis is carried out under the influence of full set-up parameters and for both the $2π$ and $4π$ periodic currents. The present study is expected to be relevant to future exploration of applications of the Majorana-nanowire circuits.

cond-mat.mes-hall↗

arXiv2016

Quantum trajectories under frequent measurements in non-Markovian environment

In this work we generalize the quantum trajectory (QT) theory from Markovian to non-Markovian environments. We model the non-Markovian environment by using a Lorentzian spectral density function with bandwidth ($Λ$), and find perfect "scaling" property with the measurement frequency ($τ^{-1}$) in terms of the scaling variable $x=Λτ$. Our result bridges the gap between the existing QT theory and the Zeno effect, by rendering them as two extremes corresponding to $x\to\infty$ and $x\to 0$, respectively. This $x$-dependent criterion improves the idea of using $τ$ alone, and quantitatively identifies the validity condition of the conventional QT theory.

quant-ph↗

arXiv2016

Qubit state tomography in superconducting circuit via weak measurements

The standard method of "measuring" quantum wavefunction is the technique of {\it indirect} quantum state tomography. Owing to conceptual novelty and possible advantages, an alternative {\it direct} scheme was proposed and demonstrated recently in quantum optics system. In this work we present a study on the direct scheme of measuring qubit state in the circuit QED system, based on weak measurement and weak value concepts. To be applied to generic parameter conditions, our formulation and analysis are carried out for finite strength weak measurement, and in particular beyond the bad-cavity and weak-response limits. The proposed study is accessible to the present state-of-the-art circuit-QED experiments.

quant-ph↗

arXiv2016

Number-resolved master equation approach to quantum measurement and quantum transport

In addition to the well-known Landauer-Buttiker scattering theory and the nonequilibrium Green's function technique for mesoscopic transports, an alternative (and very useful) scheme is quantum master equation approach. In this article, we review the particle-number (n)-resolved master equation (n-ME) approach and its systematic applications in quantum measurement and quantum transport problems. The n-ME contains rich dynamical information, allowing efficient study of topics such as shot noise and full counting statistics analysis. Moreover, we also review a newly developed master equation approach (and its n-resolved version) under self-consistent Born approximation. The application potential of this new approach is critically examined via its ability to recover the exact results for noninteracting systems under arbitrary voltage and in presence of strong quantum interference, and the challenging non-equilibrium Kondo effect.

quant-ph↗

arXiv2016

Simple understanding of quantum weak values

In this work we revisit the important and controversial concept of quantum weak values, aiming to provide a simplified understanding to its associated physics and the origin of anomaly. Taking the Stern-Gerlach setup as a working system, we base our analysis on an exact treatment in terms of quantum Bayesian approach. We also make particular connection with a very recent work, where the anomaly of the weak values was claimed from the pure statistics in association with "disturbance" and "post-selection", rather than the unique quantum nature. Our analysis resolves the related controversies through a clear and quantitative way.

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