arXiv subjects

Jukka P. Pekola

Publications and source records attributed to Jukka P. Pekola.

At least 37 records · Page 2Linked to original sources

arXiv2023

Long-time relaxation of a finite spin bath linearly coupled to a qubit

We discuss the long-time relaxation of a qubit linearly coupled to a finite bath of $N$ spins (two-level systems, TLSs), with the interaction Hamiltonian in rotating wave approximation. We focus on the regime $N\gg 1$, assuming that the qubit-bath coupling is weak, that the range of spin frequencies is sufficiently broad, and that all the spins are initialized in the ground state. Despite the model being perfectly integrable, we make two interesting observations about the effective system relaxation. First, as one would expect, the qubit relaxes exponentially towards its zero-temperature state at a well characterized rate. Second, the bath spins, even when mutually coupled, do not relax towards a thermal distribution, but rather form a Lorentzian distribution peaked at the frequency of the initially excited qubit. This behavior is captured by an analytical approximation that makes use of the property $N\gg 1$ to treat the TLS frequencies as a continuum and is confirmed by our numerical simulations.

quant-ph↗

arXiv2023

Optimized proximity thermometer for ultrasensitive detection: Role of an ohmic electromagnetic environment

We propose a mesoscopic thermometer for ultrasensitive detection based on the proximity effect in superconductor-normal metal (SN) heterostructures. The device is based on the zero-bias anomaly due to the inelastic Cooper pair tunneling in an SNIS junction (I stands for an insulator) coupled to an ohmic electromagnetic (EM) environment. The theoretical model is done in the framework of the quasiclassical Usadel Green's formalism and the dynamical Coulomb blockade. The usage of an ohmic EM environment makes the thermometer highly sensitive down to very low temperatures, $T \lesssim 5~$mK. Moreover, defined in this way, the thermometer is stable against small but nonvanishing voltage amplitudes typically used for measuring the zero-bias differential conductance in experiments. Finally, we propose a simplified view, based on an analytic treatment, which is in very good agreement with numerical results and can serve as a tool for the development, calibration, and optimization of such devices in future experiments in quantum calorimetry.

cond-mat.mes-hall↗

arXiv2023

Dynamical phase and quantum heat at fractional frequencies

We demonstrate a genuine quantum feature of heat: the power emitted by a qubit (quantum two-level system) into a reservoir under continuous driving shows peaks as a function of frequency $f$. These resonant features appear due to the accumulation of the dynamical phase during the driving. The position of the $n$th maximum is given by $f=f_{\rm M}/n$, where $f_{\rm M}$ is the mean frequency of the qubit in the cycle, and their positions are independent of the form of the drive and the number of heat baths attached, and even the presence or absence of spectral filtering. We show that the waveform of the drive determines the intensity of the peaks, differently for odd and even resonances. This quantum heat is expected to play a crucial role in the performance of driven thermal devices such as quantum heat engines and refrigerators. We also show that by optimizing the cycle protocol, we recover the favorable classical limit in fast driven systems without the use of counter-diabatic drive protocols and we demonstrate an entropy preserving non-unitary process. We propose that this non-trivial quantum heat can be detected by observing the steady-state power absorbed by a resistor acting as a bolometer attached to a driven superconducting qubit.

quant-ph↗

arXiv2023

Microwave quantum diode

The fragile nature of quantum circuits is a major bottleneck to scalable quantum applications. Operating at cryogenic temperatures, quantum circuits are highly vulnerable to amplifier backaction and external noise. Non-reciprocal microwave devices such as circulators and isolators are used for this purpose. These devices have a considerable footprint in cryostats, limiting the scalability of quantum circuits. We present a compact microwave diode architecture, which exploits the non-linearity of a superconducting flux qubit. At the qubit degeneracy point we experimentally demonstrate a significant difference between the power levels transmitted in opposite directions. The observations align with the proposed theoretical model. At -99 dBm input power, and near the qubit-resonator avoided crossing region, we report the transmission rectification ratio exceeding 90% for a 50 MHz wide frequency range from 6.81 GHz to 6.86 GHz, and over 60% for the 250 MHz range from 6.67 GHz to 6.91 GHz. The presented architecture is compact, and easily scalable towards multiple readout channels, potentially opening up diverse opportunities in quantum information, microwave read-out and optomechanics.

quant-ph↗

arXiv2022

Fluctuations of Heat in Driven Two-State Systems: Application to Single-Electron Box with Superconducting Gap

We use trajectory averaging to show that the energy dissipated in the nonequilibrium energy-state transitions of a driven two-state system satisfies a fluctuation-dissipation relation. This connection between the average energy dissipation induced by external driving and its fluctuations about equilibrium is preserved by an adiabatic approximation scheme. We use this scheme to obtain the heat statistics of a single-electron box with superconducting leads in the slow-driving regime, where the dissipated heat becomes normally distributed with a relatively high probability to be extracted from the environment rather than dissipated. We also discuss heat fluctuation relations for driven two-state transitions.

cond-mat.mes-hall↗

arXiv2022

Suppression of back-tunnelling events in hybrid single-electron turnstiles by source-drain bias modulation

Accuracy of single-electron currents produced in hybrid turnstiles at high operation frequencies is, among other errors, limited by electrons tunnelling in the wrong direction. Increasing the barrier transparency between the island and the leads, and the source-drain bias helps to suppress these events in a larger frequency range, although they lead to some additional errors. We experimentally demonstrate a driving scheme that suppresses tunnelling in the wrong direction hence extending the range of frequencies for generating accurate single-electron currents. The main feature of this approach is an additional AC signal applied to the bias with twice the frequency as the one applied to the gate electrode. This allows additional modulation of the island chemical potential. By using the new approach under certain parameters, we improve the single-electron current accuracy by one order of magnitude. Finally, we show through experimentally-contrasted calculations that our method can improve accuracy even in devices for which the usual gate driving gives errors $\sim 10^{-3}$ at high frequencies and can bring them under $5\times 10^{-4}$.

cond-mat.mes-hall↗

arXiv2022

Zero-average bias bidirectional single-electron current generation in a hybrid turnstile

Hybrid turnstiles have proven to generate accurate single-electron currents. The usual operation consists of applying a periodic modulation to a capacitively coupled gate electrode and requires a non-zero DC source-drain bias voltage. Under this operation, a current of the same magnitude and opposite direction can be generated by flipping the polarity of the bias. Here, we demonstrate that accurate single-electron currents can be generated under zero average bias voltage. We achieve this by applying an extra periodic modulation with twice the frequency of the gate signal and zero DC level to the source electrode. This creates a time interval, which is otherwise zero, between the crossings of tunnelling thresholds that enable single-electron tunnelling. Furthermore, we show that within this operation the current direction can be reversed by only shifting the phase of the source signal.

cond-mat.mes-hall↗

arXiv2022

Electromagnetic Simulation and Microwave Circuit Approach of Heat Transport in Superconducting Qubits

The study of quantum heat transport in superconducting circuits is significant for further understanding the connection between quantum mechanics and thermodynamics, and for possible applications for quantum information. The first experimental realisations of devices demonstrating photonic heat transport mediated by a qubit have already been designed and measured. Motivated by the analysis of such experimental results, and for future experimental designs, we numerically evaluate the photonic heat transport of qubit-resonator devices in the linear circuit regime through electromagnetic simulations using Sonnet software, and compare with microwave circuit theory. We show that the method is a powerful tool to calculate heat transport and predict unwanted parasitic resonances and background.

quant-ph↗

arXiv2022

A Cooper-Pair Box Coupled to Two Resonators: An Architecture for a Quantum Refrigerator

Superconducting circuits present a promising platform with which to realize a quantum refrigerator. Motivated by this, we fabricate and perform spectroscopy of a gated Cooper-pair box, capacitively coupled to two superconducting coplanar waveguide resonators with different frequencies. We experimentally demonstrate the strong coupling of a charge qubit to two superconducting resonators, with the ability to perform voltage driving of the qubit at GHz frequencies. We go on to discuss how the measured device could be modified to operate as a cyclic quantum refrigerator by terminating the resonators with normal-metal resistors acting as heat baths.

quant-ph↗

arXiv2022

Ultimate accuracy of frequency to power conversion by single-electron injection

We analyze theoretically the properties of the recently introduced and experimentally demonstrated converter of frequency to power. The system is composed of a hybrid single-electron box with normal island and superconducting lead, and the detector of the energy flow using a thermometer on a normal metal bolometer. Here we consider its potential for metrology. The errors in power arise mainly from inaccuracy of injecting electrons at the precise energy equal to the energy gap of the superconductor. We calculate the main systematic error in form of the excess average energy of the injected electrons and its cumulants, and due to sub-gap leakage. We demonstrate by analytic and numerical calculations that the systematic error in detection can, in principle, be made much smaller than the injection errors, which also, with proper choice of system parameters, can be very small, < 1 %, at low enough temperature. Finally we propose a simplified configuration for metrological purposes.

cond-mat.mes-hall↗

arXiv2022

Robust strong coupling architecture in circuit quantum electrodynamics

We report on a robust method to achieve strong coupling between a superconducting flux qubit and a high-quality quarter-wavelength coplanar waveguide resonator. We demonstrate the progression from the strong to ultrastrong coupling regime by varying the length of a shared inductive coupling element, ultimately achieving a qubit-resonator coupling strength of 655 MHz, $10\%$ of the resonator frequency. We derive an analytical expression for the coupling strength in terms of circuit parameters and also discuss the maximum achievable coupling within this framework. We experimentally characterize flux qubits coupled to superconducting resonators using one and two-tone spectroscopy methods, demonstrating excellent agreement with the proposed theoretical model.

quant-ph↗

arXiv2022

Local and non-local two-electron tunneling processes in a Cooper pair splitter

We measure the tunneling rates and coupling coefficients for local Andreev, non-local Andreev and elastic cotunneling processes. The non-local Andreev process, giving rise to Cooper pair splitting, exhibits the same coupling coefficient as the elastic co-tunneling whereas the local Andreev process is more than two orders of magnitude stronger than the corresponding non-local one. Theory estimates describe the findings and explain the large difference in the non-local and local coupling arising from competition between electron diffusion in the superconductor and tunnel junction transparency.

cond-mat.mes-hall↗

arXiv2021

Ultrasensitive calorimetric detection of single photons from qubit decay

We describe a qubit linearly coupled to a heat bath, either directly or via a cavity. The main focus of the paper is on calorimetric detection in a realistic circuit, specifically a solid-state qubit coupled to a resistor as an absorber. The bath in the model is formed of oscillators initially in the ground state with a distribution of energies and coupling strengths. A direct numerical solution of the Schrödinger equation for the full system including up to $10^6$ oscillators in the bath verifies the expected decay process. We address quantitatively the question of separation of the qubit and bath by adding a cavity in between which by detuning allows one to adjust the decay rate into a convenient regime for detection purposes. Most importantly, we propose splitting a quantum to two uncoupled baths and performing a cross-correlation measurement of their temperatures. This technique enhances significantly the signal-to-noise ratio of the calorimeter.

quant-ph↗

arXiv2021

Influence of device non-uniformities on the accuracy of Coulomb blockade thermometry

We investigate temperature errors of Coulomb blockade thermometer (CBT) arising from inevitable non-uniformities in tunnel junction arrays. The errors are proportional to the junction resistance variance in the universal operation regime and this result holds approximately also beyond this originally studied high temperature range. We present both analytical and numerical results, and discuss briefly their implications on achievable uniformity based on state-of-the-art fabrication of sensors.

cond-mat.mes-hall↗

arXiv2021

Photonic heat transport in three terminal superconducting circuit

Quantum heat transport devices are currently intensively studied in theory. Experimental realization of quantum heat transport devices is a challenging task. So far, they have been mostly investigated in experiments with ultra-cold atoms and single atomic traps. Experiments with superconducting qubits have also been carried out and heat transport and heat rectification has been studied in two terminal devices. The structures with three independent terminals offer additional opportunities for realization of heat transistors, heat switches, on-chip masers and even more complicated devices. Here we report an experimental realization of a three-terminal photonic heat transport device based on a superconducting quantum circuit. Its central element is a flux qubit made of a superconducting loop containing three Josephson junctions, which is connected to three resonators terminated by resistors. By heating one of the resistors and monitoring the temperatures of the other two, we determine photonic heat currents in the system and demonstrate their tunability by magnetic field at the level of 1 aW. We determine system parameters by performing microwave transmission measurements on a separate nominally identical sample and, in this way, demonstrate clear correlation between the level splitting of the qubit and the heat currents flowing through it. Our experiment is an important step in the development of on-chip quantum heat transport devices. On the one hand, such devices are of great interest for fundamental science because they allow one to investigate the effect of quantum interference and entanglement on the transport of heat. On the other hand, they also have great practical importance for the rapidly developing field of quantum computing, in which management of heat generated by qubits is a problem.

cond-mat.mes-hall↗

arXiv2021

Radio frequency Coulomb blockade thermometry

We present a scheme and demonstrate measurements of a Coulomb blockade thermometer (CBT) in a microwave transmission setup. The sensor is embedded in an $LCR$ resonator, where $R$ is determined by the conductance of the junction array of the CBT. A transmission measurement yields a signal that is directly proportional to the conductance of the CBT, thus enabling the calibration-free operation of the thermometer. This is verified by measuring an identical sensor simultaneously in the usual dc setup. The important advantage of the rf measurement is its speed: the whole bias dependence of the CBT conductance can now be measured in a time of about 100\,ms, which is thousand times faster than in a standard dc measurement. The achieved noise equivalent temperature of this first rf primary measurement is about 1 mK/$\sqrt{\rm Hz}$ at the bath temperature $T=200\,$mK.

cond-mat.mes-hall↗

arXiv2021

Frequency to power conversion by an electron turnstile

Direct frequency to power conversion (FPC), to be presented here, links both quantities through a known energy, like single-electron transport relates an operation frequency $f$ to the emitted current $I$ through the electron charge $e$ as $I=ef$. FPC is a natural candidate for a power standard resorting to the most basic definition of the watt -- energy, which is traceable to Planck's constant $h$, emitted per unit of time. This time is in turn traceable to the unperturbed ground state hyperfine transition frequency of the caesium 133 atom $Δν_\mathrm{Cs}$; hence, FPC comprises a simple and elegant way to realize the watt. In this spirit, single-photon emission and detection at known rates have been proposed and experimented as radiometric standard. However, nowadays power standards are only traceable to electrical units, i.e., volt and ohm. In this letter, we demonstrate the feasibility of an alternative proposal based on solid-state direct FPC using a SINIS (S = superconductor, N = normal metal, I = insulator) single-electron transistor (SET) accurately injecting $N$ (integer) quasiparticles (qps) per cycle to both leads with discrete energies close to their superconducting gap $Δ$, even at zero drain-source voltage. Furthermore, the bias voltage plays an important role in the distribution of the power among the two leads, allowing for an almost equal injection $NΔf$ to the two. We estimate that under appropriate conditions errors can be well below $1\%$.

cond-mat.mes-hall↗

arXiv2021

Down-conversion of quantum fluctuations of photonic heat current in a circuit

We discuss the non-zero frequency noise of heat current with the explicit example of energy carried by thermal photons in a circuit. Instead of the standard circuit modelling that gives a convenient way of predicting time-averaged heat current, we describe a setup composed of two resistors forming the heat baths by collections of bosonic oscillators. In terms of average heat transport this model leads to identical results with the conventional one, but besides this, it yields a convenient way of dealing with noise as well. The non-zero frequency heat current noise does not vanish in equilibrium even at zero temperature, the result that is known for, e.g., electron tunneling. We present a modulation method that can convert the difficult-to-measure high frequency quantum noise down to zero frequency.

cond-mat.mes-hall↗