arXiv subjects

Christian Flindt

Publications and source records attributed to Christian Flindt.

At least 19 recordsLinked to original sources

arXiv2026

Quantum transport in Cooper pair splitters using hierarchical equations of motion

We investigate charge transport in Cooper pair splitters beyond the weak-coupling and Markovian limits. To this end, we employ hierarchical equations of motion (HEOM), which can capture the combined effects of strong coupling to the leads, nonperturbative interactions, and finite voltage and temperature differences. Within this framework, we compute the electric currents as functions of the level positions of a Cooper pair splitter for various voltage and temperature configurations. In the large-bias regime, our results reduce to analytical expressions obtained from a Markovian Lindblad equation. However, recent experiments were conducted with finite voltage or temperature differences, where a Markovian description may not suffice. In this regime, HEOM yield quantitative agreement with the measured currents. We can also account for an experimentally observed thermoelectric effect in Cooper pair splitters. Our results show that HEOM provide a useful framework for describing nonequilibrium quantum transport in Cooper pair splitters and related hybrid devices.

cond-mat.mes-hall↗

arXiv2026

Generation of heat pulses in mesoscopic conductors using light fields

We propose to generate heat pulses in mesoscopic conductors using light fields. In contrast to single-electron excitations such as levitons, which are created by accurate voltage drives, our approach relies on modulating the temperature of an electronic reservoir. To this end, we show that the interactions with a light field can induce a controllable time-dependent temperature in an electrode. The temperature modulations generate charge-neutral heat pulses that can be emitted into a mesoscopic conductor and detected in the outputs. We illustrate our approach by evaluating the time-dependent currents and their fluctuations using a tight-binding model of two electronic reservoirs connected by a quantum point contact. Our work establishes a route towards on-demand caloritronics, where energy rather than charge carries quantum information, and it paves the way for probing time-resolved heat transport and quantum coherence in thermally driven conductors.

cond-mat.mes-hall↗

arXiv2026

Heat, work, and fluctuations in a driven quantum resonator

A central building block of a heat engine is the working fluid, which mediates the conversion of heat into work. In nanoscale heat engines, the working fluid can be a quantum system whose behavior and dynamics are non-classical. A particularly versatile realization is a quantum resonator, which allows for precise control and coupling to thermal reservoirs, making it an ideal platform for exploring quantum thermodynamic processes. Here, we investigate the thermodynamic properties of a driven quantum resonator whose temperature is controlled by modulating its natural frequency. We evaluate the work performed by the external drive and the resulting heat flow between the resonator and its environment, both within linear response and beyond. To further elucidate these processes, we determine the full distribution of photon exchanges between the resonator and its environment, characterized by its first few cumulants. Our results provide quantitative insights into the interplay between heat, work, and fluctuations, and may help in designing future heat engines.

quant-ph↗

arXiv2025

Current cross-correlation spectroscopy of Majorana bound states

The clock speed of topological quantum computers based on Majorana zero mode (MZM)-supporting nanoscale devices is limited by the time taken for electrons to traverse the device. We employ the time-dependent Landauer-B{\"u}ttiker transport theory for current cross-lead correlations in a superconducting nanowire junction hosting MZMs. From the time-dependent quantum noise, we are able to extract traversal times for electrons crossing the system. After demonstrating a linear scaling of traversal times with nanowire length, we present a heuristic formula for the traversal times which accurately captures their behaviour. We then connect our framework to a proposed experimental verification of this discriminant between spurious and genuine MZMs utilizing time-resolved transport measurements.

cond-mat.mes-hall↗

arXiv2025

Full counting statistics and first-passage times in quantum Markovian processes: Ensemble relations, metastability, and fluctuation theorems

We develop a comprehensive framework for characterizing fluctuations in quantum transport and nonequilibrium thermodynamics using two complementary approaches: full counting statistics and first-passage times. Focusing on open quantum systems governed by Markovian Lindblad dynamics, we derive general ensemble relations that connect the two approaches at all times, and we clarify how the steady states reached at long times relate to those reached at large jump counts. In regimes of metastability, long-lived intermediate states cause violations of experimentally testable cumulant relations, as we discuss. We also formulate a fluctuation theorem governing the probability of rare fluctuations in the first-passage time distributions based on results from full counting statistics. Our results apply to general integer-valued trajectory observables that do not necessarily increase monotonically in time. Three illustrative applications, a two-state emitter, a driven qubit, and a variant of the Su-Schrieffer-Heeger model, highlight the physical implications of our results and provide guidelines for practical calculations. Our framework provides a complete picture of first-passage time statistics in Markovian quantum systems, encompassing multiple earlier results, and it has direct implications for current experiments in quantum optics, superconducting circuits, and nanoscale heat engines.

cond-mat.stat-mech↗

arXiv2025

Floquet-Nambu theory of electron quantum optics with superconductors

We present a comprehensive Floquet-Nambu theory to describe the time-dependent quantum transport in mesoscopic circuits involving superconductors. The central object of our framework is the first-order correlation function, which accounts for the excitations that are generated by a time-dependent voltage and their coherent scattering off the interface with a superconductor. We analyze the time-dependent current generated by periodic voltage pulses and how it depends on the excitation energies of the voltage drive compared to the gap of the superconductor. Our general formalism allows us to identify the conditions for the excitations that are scattered off the superconductor to become coherent electron-hole superpositions. To this end, we consider the purity of the outgoing states, which characterizes their ability to carry quantum information. To illustrate our formalism, we apply it to a system composed of chiral quantum Hall edge states connected to a superconductor, and we calculate the current in the outgoing lead and the purity of the outgoing states for Lorentzian and harmonic voltage drives. Our framework paves the way for systematic investigations of time-dependent scattering problems involving superconductivity, and it may help interpret future experiments in electron quantum optics with superconductors.

cond-mat.mes-hall↗

arXiv2025

Negative currents in Fabry-P\'erot cavities are caused by interfering paths

It has been predicted that the time-dependent current in a Fabry-P\'erot cavity can turn negative even if the applied voltage pulses are always positive. It has also been suggested that the negative currents are related to interfering paths, however, an analytic description of this surprising phenomenon has so far been missing. Here we make use of Floquet scattering theory to demonstrate that the negative currents indeed are caused by the interference of scattering paths through the cavity with different numbers of roundtrips. Our analytic result can be tested in future experiments as it predicts exactly how the effect should be washed out by an increasing temperature. We show that a similar phenomenon is expected for the heat current, which may also turn negative.

cond-mat.mes-hall↗

arXiv2024

Fast, Accurate, and Local Temperature Control Using Qubits

Many quantum technologies, including quantum computers, quantum heat engines, and quantum sensors, rely on operating conditions in the subkelvin regime. It is therefore desirable to develop practical tools and methods for the precise control of the temperature in nanoscale quantum systems. Here, we present a proposal for fast, accurate, and local temperature control using qubits, which regulate the flow of heat between a quantum system and its thermal environment. The qubits are kept in a thermal state with a temperature that is controlled in an interplay between work done on the qubits by changing their energy splittings and the flow of heat between the qubits and the environment. Using only a few qubits, it is possible to control the thermal environment of another quantum system, which can be heated or cooled by the qubits. As an example, we show how a quantum system at subkelvin temperatures can be significantly and accurately cooled on a nanosecond timescale. Our proposal can potentially be realized with superconducting flux qubits, charge qubits, or spin qubits, which can now be fabricated and manipulated with exquisite control.

cond-mat.mes-hall↗

arXiv2024

Lee-Yang formalism for phase transitions of interacting fermions using tensor networks

Predicting the phase diagram of interacting quantum many-body systems is a challenging problem in condensed matter physics. Strong interactions and correlation effects may lead to exotic states of matter, such as quantum spin liquids and unconventional superconductors, that often compete with other symmetry broken states including ordered magnets and charge density waves. Here, we put forward a formalism for determining the phase diagram of fermionic systems that combines recent progress in the field of Lee-Yang theory of phase transitions with many-body tensor-network methods. Using this strategy, we map out the phase diagram of a fermionic chain, where charge density waves form owing to strong repulsion. Specifically, from the high cumulants of the order parameter, we extract the dominant zeros of the moment-generating function in chains of finite size. By extrapolating their positions to the thermodynamic limit, we determine the boundaries between competing phases. Our formalism provides a strategy for determining critical points in fermionic systems, and it is based on fluctuations of the order parameter, which are measurable quantities.

cond-mat.str-el↗

arXiv2024

Photon counting statistics in Gaussian bosonic networks

The statistics of transmitted photons in microwave cavities play a foundational role in microwave quantum optics and its technological applications. By utilizing quantum mechanical phase-space methods, we here develop a general theory of the photon counting statistics in Gaussian bosonic networks consisting of driven cavities with beamsplitter interactions and two-mode-squeezing. The dynamics of the network can be captured by a Lyapunov equation for the covariance matrix of the cavity fields, which generalizes to a Riccati equation, when counting fields are included. By solving the Riccati equation, we obtain the statistics of emitted and absorbed photons as well as the time-dependent correlations encoded in waiting time distributions and second-order coherence functions. To illustrate our theoretical framework, we first apply it to a simple linear network consisting of two coupled cavities, for which we evaluate the photon cross-correlations and discuss connections between the photon emission statistics and the entanglement between the cavities. We then consider a bosonic circulator consisting of three coupled cavities, for which we investigate how a synthetic flux may affect the direction of the photon flow, similarly to recent experiments. Our general framework paves the way for systematic investigations of the photon counting statistics in Gaussian bosonic networks.

cond-mat.mes-hall↗

arXiv2024

Real-Time Detection and Control of Correlated Charge Tunneling in a Quantum Dot

We experimentally demonstrate the real-time detection and control of correlated charge tunneling in a dynamically driven quantum dot. Specifically, we measure the joint distribution of waiting times between tunneling charges and show that the waiting times for holes may be strongly correlated due to the periodic drive and the Coulomb interactions on the dot, although the electron waiting times are not. Our measurements are in excellent agreement with a theoretical model that allows us to develop a detailed understanding of the correlated tunneling events. We also demonstrate that the degree of correlations can be controlled by the drive. Our experiment paves the way for systematic real-time investigations of correlated electron transport in low-dimensional nanostructures.

cond-mat.mes-hall↗

arXiv2024

Lee-Yang theory of the superradiant phase transition in the open Dicke model

The Dicke model describes an ensemble of two-level atoms that are coupled to a confined light mode of an optical cavity. Above a critical coupling, the cavity becomes macroscopically occupied, and the system enters the superradiant phase. This phase transition can be observed by detecting the photons that are emitted from the cavity; however, it only becomes apparent in the limit of long observation times, while actual experiments are of a finite duration. To circumvent this problem, we here make use of recent advances in Lee-Yang theories of phase transitions to show that the superradiant phase transition can be inferred from the factorial cumulants of the photon emission statistics obtained during a finite measurement time. Specifically, from the factorial cumulants, we can determine the complex singularities of generating functions that describe the photon emission statistics, and by extrapolating their positions to the long-time limit, one can detect the superradiant phase transition. We also show that the convergence points determine the tails of the large-deviation statistics of the photon current. Our work demonstrates how phase transitions in the Dicke model and in other quantum many-body systems can be detected from measurements of a finite duration.

cond-mat.mes-hall↗

arXiv2024

Quantum computing topological invariants of two-dimensional quantum matter

Quantum algorithms provide a potential strategy for solving computational problems that are intractable by classical means. Computing the topological invariants of topological matter is one central problem in research on quantum materials, and a variety of numerical approaches for this purpose have been developed. However, the complexity of quantum many-body Hamiltonians makes calculations of topological invariants challenging for interacting systems. Here, we present two quantum circuits for calculating Chern numbers of two-dimensional quantum matter on quantum computers. Both circuits combine a gate-based adiabatic time-evolution over the discretized Brillouin zone with particular phase estimation techniques. The first algorithm uses many qubits, and we analyze it using a tensor-network simulator of quantum circuits. The second circuit uses fewer qubits, and we implement it experimentally on a quantum computer based on superconducting qubits. Our results establish a method for computing topological invariants with quantum circuits, taking a step towards characterizing interacting topological quantum matter using quantum computers.

quant-ph↗

arXiv2023

Wigner representation of Andreev-reflected charge pulses

Recent experiments have shown that the edge states of a quantum Hall sample can be coupled to a superconductor, so that incoming electrons in the edge states can be Andreev converted by the superconductor as coherent superpositions of an electron and a hole. In parallel, single-electron emitters that operate in the gigahertz regime have been realized on quantum Hall edge states. Motivated by this remarkable experimental progress, we here analyze the Andreev reflections of incoming charge pulses on the interface with a superconductor. To this end, we employ a Wigner function representation that allows us to visualize the response function of the interface both in the time and in the frequency domain. We analyze the response of an interface between a normal-metal and a singlet or triplet superconductor with and without an insulating barrier in between them. As a special case, we analyze the Andreev reflections of clean single-particle excitations that are generated by the application of lorentzian-shaped voltage pulses to the contacts of the inputs. Our predictions may be tested in future experiments with edge states coupled to superconductors.

cond-mat.mes-hall↗

arXiv2023

On-Demand and Tunable Andreev-Conversion of Single-Electron Charge Pulses

Electron quantum optics explores coherent single-electron charge pulse propagation in electronic nanoscale circuits akin to table-top photon setups. While past experiments focused on normal-state conductors, incorporating superconductors holds promise for exploiting the electron-hole degree of freedom in quantum sensing applications and quantum information processing. Here, we propose and analyze an on-demand and tunable mechanism for converting single-electron pulses into holes through Andreev processes on a superconductor. We develop a Floquet-Nambu scattering formalism to demonstrate the dynamic conversion of charge pulses and the controllable generation of coherent electron-hole superpositions through interferometric magnetic flux control based on the chiral edge states of a quantum Hall sample. Our discussion covers optimal conditions in realistic scenarios, affirming the feasibility of our proposal with current technology.

cond-mat.mes-hall↗

arXiv2023

Heat Pulses in Electron Quantum Optics

Electron quantum optics aims to realize ideas from the quantum theory of light with the role of photons being played by charge pulses in electronic conductors. Experimentally, the charge pulses are excited by time-dependent voltages, however, one could also generate heat pulses by heating and cooling an electrode. Here, we explore this intriguing idea by formulating a Floquet scattering theory of heat pulses in mesoscopic conductors. The adiabatic emission of heat pulses leads to a heat current that in linear response is given by the thermal conductance quantum. However, we also find a high-frequency component, which ensures that the fluctuation-dissipation theorem for heat currents, whose validity has been debated, is fulfilled. The heat pulses are uncharged, and we probe their electron-hole content by evaluating the partition noise in the outputs of a quantum point contact. We also employ a Hong--Ou--Mandel setup to examine if the pulses bunch or antibunch. Finally, to generate an electric current, we use a Mach--Zehnder interferometer that breaks the electron-hole symmetry and thereby enables a thermoelectric effect. Our work paves the way for systematic investigations of heat pulses in mesoscopic conductors, and it may stimulate future experiments.

cond-mat.mes-hall↗

arXiv2023

Lee-Yang theory of quantum phase transitions with neural network quantum states

Predicting the phase diagram of interacting quantum many-body systems is a central problem in condensed matter physics and related fields. A variety of quantum many-body systems, ranging from unconventional superconductors to spin liquids, exhibit complex competing phases whose theoretical description has been the focus of intense efforts. Here, we show that neural network quantum states can be combined with a Lee-Yang theory of quantum phase transitions to predict the critical points of strongly-correlated spin lattices. Specifically, we implement our approach for quantum phase transitions in the transverse-field Ising model on different lattice geometries in one, two, and three dimensions. We show that the Lee-Yang theory combined with neural network quantum states yields predictions of the critical field, which are consistent with large-scale quantum many-body methods. As such, our results provide a starting point for determining the phase diagram of more complex quantum many-body systems, including frustrated Heisenberg and Hubbard models.

cond-mat.str-el↗

arXiv2023

Photon emission statistics of a driven microwave cavity

Recent experimental advances have made it possible to detect individual quantum jumps in open quantum systems, such as the tunneling of single electrons in nanoscale conductors or the emission of photons from non-classical light sources. Here, we investigate theoretically the statistics of photons emitted from a microwave cavity that is driven resonantly by an external field. We focus on the differences between a parametric and a coherent drive, which either squeezes or displaces the cavity field. We employ a Lindblad master equation dressed with counting fields to obtain the generating function of the photon emission statistics using a theoretical framework based on Gaussian states. We then compare the distribution of photon waiting times for the two drives as well as the $g^{(2)}$-functions of the outgoing light, and we identify important differences between these observables. In the long-time limit, we analyze the factorial cumulants of the photon emission statistics and the large-deviation statistics of the emission currents, which are markedly different for the two drives. Our theoretical framework can readily be extended to more complicated systems, for instance, with several coupled microwave cavities, and our predictions may be tested in future experiments.

cond-mat.mes-hall↗