arXiv subjects

G. Rastelli

Publications and source records attributed to G. Rastelli.

At least 19 recordsLinked to original sources

arXiv2024

Synthetic-lattice Bloch wave dynamics in a single-mode microwave resonator

Frequency-based synthetic dimensions are a promising avenue for expanding the dimensionality of photonic systems. In this work, we show how a tilted synthetic lattice is naturally realised by periodically modulating a single-mode resonator under a coherent monochromatic drive. We theoretically study the Bloch wave dynamics in the tilted synthetic lattice, which gives rise to peculiar features in the spectral distribution of the cavity field. Our predictions are experimentally confirmed using a planar tunable superconducting microwave resonator.

cond-mat.mes-hall↗

arXiv2024

Nonlinearity-induced symmetry breaking in a system of two parametrically driven Kerr-Duffing oscillators

We study the classical dynamics of a system comprising a pair of Kerr-Duffing nonlinear oscillators, which are coupled through a nonlinear interaction and subjected to a parametric drive. Using the rotating wave approximation (RWA), we analyze the steady-state solutions for the amplitudes of the two oscillators. For the case of almost identical oscillators, we investigate separately the cases in which only one oscillator is parametrically driven and in which both oscillators are simultaneously driven. In the latter regime, we demonstrate that even when the parametric drives acting on the two oscillators are identical, the system can transition from a stable Nesymmetric solution to a broken-symmetry solution as the detuning is varied.

physics.class-ph↗

arXiv2022

Tunneling processes between Yu-Shiba-Rusinov bound states

Very recent experiments have reported the tunneling between Yu-Shiba-Rusinov (YSR) bound states at the atomic scale. These experiments have been realized with the help of a scanning tunneling microscope where a superconducting tip is functionalized with a magnetic impurity and is used to probe another magnetic impurity deposited on a superconducting substrate. In this way it has become possible to study for the first time the spin-dependent transport between individual superconducting bound states. Motivated by these experiments, we present here a comprehensive theoretical study of the tunneling processes between YSR bound states in a system in which two magnetic impurities are coupled to superconducting leads. Our theory is based on a combination of an Anderson model with broken spin degeneracy to describe the impurities and nonequilibrium Green's function techniques to compute the current-voltage characteristics. This combination allows us to describe the spin-dependent transport for an arbitrary strength of the tunnel coupling between the impurities. We first focus on the tunnel regime and show that our theory naturally explains the experimental observations of the appearance of current peaks in the subgap region due to both the direct and thermal tunneling between the YSR states in both impurities. Then, we study in detail the case of junctions with increasing transparency, which has not been experimentally explored yet, and predict the occurrence of a large variety of (multiple) Andreev reflections mediated by YSR states that give rise to a very rich structure in the subgap current. In particular, we predict the occurrence of multiple Andreev reflections that involve YSR states in different impurities. These processes have no analogue in single-impurity junctions and they are manifested as current peaks with negative differential conductance for subgap voltages.

cond-mat.supr-con↗

arXiv2022

Frequency comb from a single driven nonlinear nanomechanical mode

Phononic frequency combs have been attracting an increasing attention both as a qualitatively new type of nonlinear phenomena in vibrational systems and from the point of view of applications. It is commonly believed that at least two modes must be involved in generating a comb. In this paper we demonstrate that a comb can be generated by a single nanomechanical mode driven by a resonant monochromatic drive. The comb emerges where the drive is still weak, so that the anharmonic part of the mode potential energy remains small. We relate the effect to a negative nonlinear friction induced by the resonant drive, which makes the vibrations at the drive frequency unstable. We directly map the trajectories of the emerging oscillations in the rotating frame and show how these oscillations lead to the frequency comb in the laboratory frame. The results go beyond nanomechanics and suggest a qualitatively new approach to generating tunable frequency combs in single-mode vibrational systems.

cond-mat.mes-hall↗

arXiv2021

Resonant nonlinear response of a nanomechanical system with broken symmetry

We study the response of a weakly damped vibrational mode of a nanostring resonator to a moderately strong resonant driving force. Because of the geometry of the experiment, the studied flexural vibrations lack inversion symmetry. As we show, this leads to a nontrivial dependence of the vibration amplitude on the force parameters. For a comparatively weak force, the response has the familiar Duffing form, but for a somewhat stronger force, it becomes significantly different. Concurrently there emerge vibrations at twice the drive frequency, a signature of the broken symmetry. Their amplitude and phase allow us to establish the cubic nonlinearity of the potential of the mode as the mechanism responsible for both observations. The developed theory goes beyond the standard rotating-wave approximation. It quantitatively describes the experiment and allows us to determine the nonlinearity parameters.

cond-mat.mes-hall↗

arXiv2020

Second Chern Number and Non-Abelian Berry Phase in Topological Superconducting Systems

Topology ultimately unveils the roots of the perfect quantization observed in complex systems. The 2D quantum Hall effect is the celebrated archetype. Remarkably, topology can manifest itself even in higher-dimensional spaces in which control parameters play the role of extra, synthetic dimensions. However, so far, a very limited number of implementations of higher-dimensional topological systems have been proposed, a notable example being the so-called 4D quantum Hall effect. Here we show that mesoscopic superconducting systems can implement higher-dimensional topology and represent a formidable platform to study a quantum system with a purely nontrivial second Chern number. We demonstrate that the integrated absorption intensity in designed microwave spectroscopy is quantized and the integer is directly related to the second Chern number. Finally, we show that these systems also admit a non-Abelian Berry phase. Hence, they also realize an enlightening paradigm of topological non-Abelian systems in higher dimensions.

cond-mat.supr-con↗

arXiv2020

Spectral Evidence of Squeezing of a Weakly Damped Driven Nanomechanical Mode

Because of the broken time-translation symmetry, in periodically driven vibrational systems fluctuations of different vibration components have different intensities. Fluctuations of one of the components are often squeezed, whereas fluctuations of the other component, which is shifted in phase by π/2, are increased. Squeezing is a multifaceted phenomenon; it attracts much attention from the perspective of high-precision measurements. Here we demonstrate a new and hitherto unappreciated side of squeezing: its direct manifestation in the spectra of driven vibrational systems. With a weakly damped nanomechanical resonator, we study the spectrum of thermal fluctuations of a resonantly driven nonlinear mode. In the attained sideband-resolved regime, we show that the asymmetry of the spectrum directly characterizes the squeezing. This opens a way to deduce squeezing of thermal fluctuations in strongly underdamped resonators, for which a direct determination by a standard homodyne measurement is impeded by frequency fluctuations. The experimental and theoretical results are in excellent agreement. We further extend the theory to also describe the spectral manifestation of squeezing of quantum fluctuations.

cond-mat.mes-hall↗

arXiv2019

Tuning the nonlinear dispersive coupling of nanomechanical string resonators

We investigate nonlinear dispersive mode coupling between the flexural in- and out-of-plane modes of two doubly clamped, nanomechanical silicon nitride string resonators. As the amplitude of one mode transitions from the linear response regime into the nonlinear regime, we find a frequency shift of two other modes. The resonators are strongly elastically coupled via a shared clamping point and can be tuned in and out of resonance dielectrically, giving rise to multimode avoided crossings. When the modes start hybridizing, their polarization changes. This affects the nonlinear dispersive coupling in a non-trivial way. We propose a theoretical model to describe the dependence of the dispersive coupling on the mode hybridization.

cond-mat.mes-hall↗

arXiv2019

Theory of double Cooper-pair tunneling and light emission mediated by a resonator

Photon emission by tunneling electrons can be encouraged by locating a resonator close to the tunnel junction and applying an appropriate voltage-bias. However, studies of normal metals show that the resonator also affects how the charges flow, facilitating processes in which correlated tunneling of two charges produces one photon. We develop a theory to analyze this kind of behavior in Josephson junctions by deriving an effective Hamiltonian describing processes where two Cooper-pairs generate a single photon. We determine the conditions under which the transport is dominated by incoherent tunneling of two Cooper-pairs, whilst also uncovering a regime of coherent double Cooper-pair tunneling. We show that the system can also display an unusual form of photon-blockade and hence could serve as a single-photon source.

cond-mat.mes-hall↗

arXiv2019

Ground state cooling of nanomechanical resonators by electron transport

We discuss two theoretical proposals for controlling the nonequilibrium steady state of nanomechanical resonators using quantum electronic transport. Specifically?, we analyse two approaches to achieve the ground-state cooling of the mechanical vibration coupled to a quantum dot embedded between (i) spin-polarised contacts or (ii) a normal metal and a superconducting contact. Assuming a suitable coupling between the vibrational modes and the charge or spin of the electrons in the quantum dot, we show that ground-state cooling of the mechanical oscillator is within the state of the art for suspended carbon nanotube quantum dots operating as electromechanical devices.

cond-mat.mes-hall↗

arXiv2016

Dissipation-induced enhancement and squeezing of quantum fluctuations

We study a quantum harmonic oscillator linearly coupled through the position operator $\hat{q}$ to a first bath and through the momentum operator $\hat{p}$ to a second bath yielding an Ohmic-Drude dissipation. We analyse the oscillator's fluctuations as a function of the ratio between the strength of the two couplings, focusing in particular on the situation in which the two dissipative interactions are comparable. Analytic formulas are derived in the relevant regimes corresponding to the low temperature limit and when the Drude high frequency cutoff is much larger than all other frequencies. At low temperature, each bath operates to suppress the oscillator's ground state quantum fluctuations ${\langle Δ\hat{q}^2 \rangle}_0$ or ${\langle Δ\hat{p}^2 \rangle}_0$ appearing in the corresponding interaction. When one of the two dissipative interactions dominates over the other, the fluctuations for the coupling operator are squeezed. When the two interactions are comparable, the two baths enter in competition as the two conjugate operators do not commute yielding quantum frustration. In this regime, remarkably, the fluctuations of both two quadratures can be enhanced by increasing the dissipative coupling.

cond-mat.mes-hall↗

arXiv2015

Coherent dynamics in long fluxonium qubits

We analyze the coherent dynamics of a fluxonium device (Manucharyan et al 2009 Science 326 113) formed by a superconducting ring of Josephson junctions in which strong quantum phase fluctuations are localized exclusively on a single weak element. In such a system, quantum phase tunnelling by $2π$ occurring at the weak element couples the states of the ring with supercurrents circulating in opposite directions, while the rest of the ring provides an intrinsic electromagnetic environment of the qubit. Taking into account the capacitive coupling between nearest neighbors and the capacitance to the ground, we show that the homogeneous part of the ring can sustain electrodynamic modes which couple to the two levels of the flux qubit. In particular, when the number of Josephson junctions is increased, several low-energy modes can have frequencies lower than the qubit frequency. This gives rise to a quasiperiodic dynamics, which manifests itself as a decay of oscillations between the two counterpropagating current states at short times, followed by oscillation-like revivals at later times. We analyze how the system approaches such a dynamics as the ring's length is increased and discuss possible experimental implications of this non-adiabatic regime.

cond-mat.mes-hall↗

arXiv2014

Bloch band dynamics of a Josephson junction in an inductive environment

We have measured the current-voltage characteristics of a Josephson junction with tunable Josephson energy $E_J$ embedded in an inductive environment provided by a chain of SQUIDs. Such an environment induces localization of the charge on the junction, which results in an enhancement of the zero-bias resistance of the circuit. We understand this result quantitatively in terms of the Bloch band dynamics of the localized charge. This dynamics is governed by diffusion in the lowest Bloch band of the Josephson junction as well as by Landau-Zener transitions out of the lowest band into the higher bands. In addition, the frequencies corresponding to the self-resonant modes of the SQUID array exceed the Josephson energy $E_J$ of the tunable junction, which results in a renormalization of $E_J$, and, as a consequence, of the effective bandwidth of the lowest Bloch band.

cond-mat.mes-hall↗

arXiv2013

Three and four-body systems in one dimension: integrability, superintegrability and discrete symmetries

Families of three-body Hamiltonian systems in one dimension have been recently proved to be maximally superintegrable by interpreting them as one-body systems in the three-dimensional Euclidean space, examples are the Calogero, Wolfes and Tramblay Turbiner Winternitz systems. For some of these systems, we show in a new way how the superintegrability is associated with their dihedral symmetry in the three-dimensional space, the order of the dihedral symmetries being associated with the degree of the polynomial in the momenta first integrals. As a generalization, we introduce the analysis of integrability and superintegrability of four-body systems in one dimension by interpreting them as one-body systems with the symmetries of the Platonic polyhedra in the four-dimensional Euclidean space. The paper is intended as a short review of recent results in the sector, emphasizing the relevance of discrete symmetries for the superintegrability of the systems considered.

math-ph↗

arXiv2013

Quantum phase-slips in Josephson junction rings

We study quantum phase-slip (QPS) processes in a superconducting ring containing N Josephson junctions and threaded by an external static magnetic flux. In a such system, a QPS consists of a quantum tunneling event connecting two distinct classical states of the phases with different persistent currents [K. A. Matveev et al., Phys. Rev. Lett. 89, 096802 (2002)]. When the Josephson coupling energy EJ of the junctions is larger than the charging energy EC = e2/2C where C is the junction capacitance, the quantum amplitude for the QPS process is exponentially small in the ratio EJ/EC. At given magnetic flux each QPS can be described as the tunneling of the phase difference of a single junction of almost 2pi, accompanied by a small harmonic displacement of the phase difference of the other N-1 junctions. As a consequence the total QPS amplitude nu is a global property of the ring. Here we study the dependence of nu on the ring size N taking into account the effect of a finite capacitance C0 to ground which leads to the appearance of low-frequency dispersive modes. Josephson and charging effects compete and lead to a nonmonotonic dependence of the ring critical current on N. For N=infty, the system converges either towards a superconducting or an insulating state, depending on the ratio between the charging energy E0 = e2/2C0 and the Josephson coupling energy EJ.

cond-mat.supr-con↗

arXiv2011

Mechanical lattice instability and thermodynamical properties in classical solids

In this paper we revisit the onset of the instability of the solid state in classical systems within self-consistent phonon theory (SCPT). Spanning the whole phase diagram versus volume and versus pressure, we identify two different kinds of mechanism: one mainly relevant at constant volume, associated with the vanishing of the SCPT solution; and one related to the disappearing at a spinodal temperature of the solid phase as a metastable energy minimum. We show how the first mechanism occurs at extremely high temperatures and it is not reflected in any singular behavior of the thermodynamical properties. In contrast, the second one appears at physical temperatures which correlate well with the melting temperature and it is signalized by the divergence of the thermal compressibility as well as of the the lattice expansion coefficient.

cond-mat.stat-mech↗

arXiv2009

Resonant magneto-conductance through a vibrating nanotube

We address the electronic resonant transport in presence of a transverse magnetic field through the single level of a suspended carbon nanotube acting as a quantum oscillator. We predict a negative magneto-conductance with a magnetic-field induced narrowing of the resonance line and a reduction of the conductance peak when the nanotube is asymmetrically contacted to the leads. At finite bias voltage we study the threshold for phonon-assisted transport.

cond-mat.mes-hall↗

arXiv2008

Finite size Berezinski-Kosterlitz-Thouless transition at grain boundaries in solid $^4$He and role of $^3$He impurities

We analyze the complex phenomenology of the Non-Classical Rotational Inertia (NCRI) observed at low temperature in solid $^4$He within the context of a two dimensional Berezinski-Kosterlitz-Thouless transition in a premelted $^4$He film at the grain boundaries. We show that both the temperature and $^3$He doping dependence of the NCRI fraction (NCRIF) can be ascribed to finite size effects induced by the finite grain size. We give an estimate of the average size of the grains which we argue to be limited by the isotopic $^3$He impurities and we provide a simple power-law relation between the NCRIF and the $^3$He concentration.

cond-mat.other↗