24 research outputs found
Photon counting statistics of a microwave cavity
The development of microwave photon detectors is paving the way for a wide
range of quantum technologies and fundamental discoveries involving single
photons. Here, we investigate the photon emission from a microwave cavity and
find that distribution of photon waiting times contains information about
few-photon processes, which cannot easily be extracted from standard
correlation measurements. The factorial cumulants of the photon counting
statistics are positive at all times, which may be intimately linked with the
bosonic quantum nature of the photons. We obtain a simple expression for the
rare fluctuations of the photon current, which is helpful in understanding
earlier results on heat transport statistics and measurements of work
distributions. Under non-equilibrium conditions, where a small temperature
gradient drives a heat current through the cavity, we formulate a
fluctuation-dissipation relation for the heat noise spectra. Our work suggests
a number of experiments for the near future, and it offers theoretical
questions for further investigation.Comment: 16 pages, 3 figures, final version as published in Phys. Rev.
Energy and temperature fluctuations in the single electron box
In mesoscopic and nanoscale systems at low temperatures, charge carriers are
typically not in thermal equilibrium with the surrounding lattice. The
resulting, non-equilibrium dynamics of electrons has only begun to be explored.
Experimentally the time-dependence of the electron temperature (deviating from
the lattice temperature) has been investigated in small metallic islands.
Motivated by these experiments we investigate theoretically the electronic
energy and temperature fluctuations in a metallic island in the Coulomb
blockade regime, tunnel coupled to an electronic reservoir, i.e. a single
electron box. We show that electronic quantum tunnelling between the island and
the reservoir, in the absence of any net charge or energy transport, induces
fluctuations of the island electron temperature. The full distribution of the
energy transfer as well as the island temperature is derived within the
framework of full counting statistics. In particular, the low-frequency
temperature fluctuations are analysed, fully accounting for charging effects
and non-zero reservoir temperature. The experimental requirements for measuring
the predicted temperature fluctuations are discussed.Comment: 20 pages, 4 figures, submitted to NJP special issue on Quantum
Thermodynamic
Adiabatic Cooper pair splitter
Recent experiments have observed Cooper pair splitting in quantum dots
coupled to superconductors, and efficient schemes for controlling and timing
the splitting process are now called for. Here, we propose and analyze an
adiabatic Cooper pair splitter that can produce a regular flow of
spin-entangled electrons in response to a time-dependent and periodic gate
voltage. The splitting process is controlled by moving adiabatically back and
forth along an avoided crossing between the empty state and the singlet state
of two quantum dots that are coupled to a superconductor, followed by the
emission of the split Cooper pairs into two normal-state drains. The scheme
does not rely on fine-tuned resonance conditions and is therefore robust
against experimental imperfections in the driving signal. We identify a range
of driving frequencies, where the output currents are quantized and
proportional to the driving frequency combined with suppressed low-frequency
noise. We also discuss the main sources of cycle-missing events and evaluate
the statistics of electrons emitted within a period of the drive as well as the
distribution of waiting times between them. Realistic parameter estimates
indicate that the Cooper pair splitter can be operated in the gigahertz regime.Comment: 6+2 pages, 4 figure
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.Comment: 6+5 pages, 4 figure
Dynamical quantum phase transitions in strongly correlated two-dimensional spin lattices following a quench
Dynamical quantum phase transitions are at the forefront of current efforts to understand quantum matter out of equilibrium. Except for a few exactly solvable models, predictions of these critical phenomena typically rely on advanced numerical methods. However, those approaches are mostly restricted to one dimension, making investigations of two-dimensional systems highly challenging. Here, we present evidence of dynamical quantum phase transitions in strongly correlated spin lattices in two dimensions. To this end, we apply our recently developed cumulant method [Phys. Rev. X11, 041018 (2021)] to determine the zeros of the Loschmidt amplitude in the complex plane of time, and we predict the crossing points of the thermodynamic lines of zeros with the real-time axis, where dynamical quantum phase transitions occur. We find the critical times of a two-dimensional quantum Ising lattice and the XYZ model with ferromagnetic or antiferromagnetic couplings. We also show how dynamical quantum phase transitions can be predicted by measuring the initial energy fluctuations, for example in quantum simulators or other engineered quantum systems.Peer reviewe
Determination of Dynamical Quantum Phase Transitions in Strongly Correlated Many-Body Systems Using Loschmidt Cumulants
Dynamical phase transitions extend the notion of criticality to nonstationary settings and are characterized by sudden changes in the macroscopic properties of time-evolving quantum systems. Investigations of dynamical phase transitions combine aspects of symmetry, topology, and nonequilibrium physics; however, progress has been hindered by the notorious difficulties of predicting the time evolution of large, interacting quantum systems. Here, we tackle this outstanding problem by determining the critical times of interacting many-body systems after a quench using Loschmidt cumulants. Specifically, we investigate dynamical topological phase transitions in the interacting Kitaev chain and in the spin-1 Heisenberg chain. To this end, we map out the thermodynamic lines of complex times, where the Loschmidt amplitude vanishes, and identify the intersections with the imaginary axis, which yield the real critical times after a quench. For the Kitaev chain, we can accurately predict how the critical behavior is affected by strong interactions, which gradually shift the time at which a dynamical phase transition occurs. We also discuss the experimental perspectives of predicting the first critical time of a quantum many-body system by measuring the energy fluctuations in the initial state, and we describe the prospects of implementing our method on a near-term quantum computer with a limited number of qubits. Our work demonstrates that Loschmidt cumulants are a powerful tool to unravel the far-from-equilibrium dynamics of strongly correlated many-body systems, and our approach can immediately be applied in higher dimensions.Dynamical phase transitions extend the notion of criticality to nonstationary settings and are characterized by sudden changes in the macroscopic properties of time-evolving quantum systems. Investigations of dynamical phase transitions combine aspects of symmetry, topology, and nonequilibrium physics; however, progress has been hindered by the notorious difficulties of predicting the time evolution of large, interacting quantum systems. Here, we tackle this outstanding problem by determining the critical times of interacting many-body systems after a quench using Loschmidt cumulants. Specifically, we investigate dynamical topological phase transitions in the interacting Kitaev chain and in the spin-1 Heisenberg chain. To this end, we map out the thermodynamic lines of complex times, where the Loschmidt amplitude vanishes, and identify the intersections with the imaginary axis, which yield the real critical times after a quench. For the Kitaev chain, we can accurately predict how the critical behavior is affected by strong interactions, which gradually shift the time at which a dynamical phase transition occurs. We also discuss the experimental perspectives of predicting the first critical time of a quantum many-body system by measuring the energy fluctuations in the initial state, and we describe the prospects of implementing our method on a near-term quantum computer with a limited number of qubits. Our work demonstrates that Loschmidt cumulants are a powerful tool to unravel the far-from-equilibrium dynamics of strongly correlated many-body systems, and our approach can immediately be applied in higher dimensions.Peer reviewe
Lee-Yang theory of Bose-Einstein condensation
Bose-Einstein condensation happens as a gas of bosons is cooled below its
transition temperature, and the ground state becomes macroscopically occupied.
The phase transition occurs in the thermodynamic limit of many particles.
However, recent experimental progress has made it possible to assemble quantum
many-body systems from bottom up, for example, by adding single atoms to an
optical lattice one at a time. Here, we show how one can predict the
condensation temperature of a Bose gas from the energy fluctuations of a small
number of bosons. To this end, we make use of recent advances in Lee-Yang
theories of phase transitions, which allow us to determine the zeros and the
poles of the partition function in the complex plane of the inverse temperature
from the high cumulants of the energy fluctuations. By increasing the number of
bosons in the trapping potential, we can predict the convergence point of the
partition function zeros in the thermodynamic limit, where they reach the
inverse critical temperature on the real axis. Using less than 100 bosons, we
can estimate the condensation temperature for a Bose gas in a harmonic
potential in two and three dimensions, and we also find that there is no phase
transition in one dimension as one would expect.Comment: 11 pages, 6 figure
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 -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.Comment: 12 pages, 6 figure
Quantum Correlations and Temperature Fluctuations in Nanoscale Systems
This thesis addresses two different topics related to the physics of nanoscale systems. The first topic concerns quantum correlations and entanglement between electrons in solid-state systems, with a focus on how to generate electronic orbital entanglement on a sub-decoherence time scale and how to achieve experimentally more feasible entanglement detection schemes. The second topic concerns heat transport and temperature fluctuations in nanoscale systems, with a focus on how to utilize temperature fluctuations for calorimetric detection of single particles. The thesis comprises five papers.In Paper I, we propose a quantum dot system to generate and detect, using cotunneling processes, orbitally entangled pairs of electrons on a sub-decoherence time scale.In Paper II, we investigate, by applying an entanglement witness, the minimal number of zero-frequency current cross-correlation measurements needed to detect bipartite entanglement between two flying qubits.In Paper III, we consider energy and temperature fluctuations, and the influence of charging effects, in a metallic island tunnel coupled to a normal metallic lead, the so-called single electron box.In Paper IV, we investigate nanoscale quantum calorimetry and propose a setup consisting of a metallic island and a superconducting lead to realize a nanoscale calorimeter that may probe the energies of tunneling electrons.In Paper V, we investigate photon transport statistics of a microwave cavity, including the short-time statistics of single photon emissions and the long-time statistics of heat transport through the cavity