arXiv subjects

Fabrizio Minganti

Publications and source records attributed to Fabrizio Minganti.

At least 37 records · Page 2Linked to original sources

arXiv2023

Dynamically crossing diabolic points while encircling exceptional curves: A programmable symmetric-asymmetric multimode switch

Nontrivial spectral properties of non-Hermitian systems can lead to intriguing effects with no counterparts in Hermitian systems. For instance, in a two-mode photonic system, by dynamically winding around an exceptional point (EP) a controlled asymmetric-symmetric mode switching can be realized. That is, the system can either end up in one of its eigenstates, regardless of the initial eigenmode, or it can switch between the two states on demand, by simply controlling the winding direction. However, for multimode systems with higher-order EPs or multiple low-order EPs, the situation can be more involved, and the ability to control asymmetric-symmetric mode switching can be impeded, due to the breakdown of adiabaticity. Here we demonstrate that this difficulty can be overcome by winding around exceptional curves by additionally crossing diabolic points. We consider a four-mode $\cal PT$-symmetric bosonic system as a platform for experimental realization of such a multimode switch. Our work provides alternative routes for light manipulations in non-Hermitian photonic setups.

physics.optics↗

arXiv2023

A critical Schrödinger cat qubit

Encoding quantum information onto bosonic systems is a promising route to quantum error correction. In a cat code, this encoding relies on the confinement of the system's dynamics onto the two-dimensional manifold spanned by Schrödinger cats of opposite parity. In dissipative cat qubits, an engineered dissipation scheme combining two-photon drive and loss has been used to autonomously stabilize this manifold, ensuring passive protection against bit-flip errors, regardless of their origin. In Kerr cat qubits, where highly-performing gates can be engineered, two-photon drive and Kerr nonlinearity cooperate to confine the system to a two-fold degenerate ground state manifold spanned by cats of opposite parity. Dissipative, Hamiltonian, and hybrid confinements have been investigated at resonance. Here, we propose a critical cat code, where both two-photon loss and Kerr nonlinearity are present, and the two-photon drive is allowed to be out of resonance. The performance of this code is assessed via the spectral theory of Liouvillians in all configurations, from the purely dissipative to the Kerr limit. We show that large detunings and small, but non-negligible, two-photon loss rates are fundamental to achieve optimal performance. We demonstrate that the competition between nonlinearity and detuning results in a first-order dissipative phase transition, leading to a squeezed vacuum steady state. To achieve the maximal suppression of the logical bit-flip rate requires initializing the system in the metastable state emerging from the first-order transition, and we detail a protocol to do so. Efficiently operating over a broad range of detuning values, the critical cat code is particularly resistant to random frequency shifts characterizing multiple-qubit operations, opening venues for the realization of reliable protocols for scalable and concatenated bosonic qubit architectures.

quant-ph↗

arXiv2023

High-kinetic inductance NbN films for high-quality compact superconducting resonators

Niobium nitride (NbN) is a particularly promising material for quantum technology applications, as entails the degree of reproducibility necessary for large-scale of superconducting circuits. We demonstrate that resonators based on NbN thin films present a one-photon internal quality factor above 10$^5$ maintaining a high impedance (larger than 2k$Ω$), with a footprint of approximately 50x100 $μ$m$^2$ and a self-Kerr nonlinearity of few tenths of Hz. These quality factors, mostly limited by losses induced by the coupling to two-level systems, have been maintained for kinetic inductances ranging from tenths to hundreds of pH/square. We also demonstrate minimal variations in the performance of the resonators during multiple cooldowns over more than nine months. Our work proves the versatility of niobium nitride high-kinetic inductance resonators, opening perspectives towards the fabrication of compact, high-impedance and high-quality multimode circuits, with sizable interactions.

quant-ph↗

arXiv2023

$n$-photon blockade with an $n$-photon parametric drive

We propose a mechanism to engineer an $n$-photon blockade in a nonlinear cavity with an $n$-photon parametric drive $λ(\hat{a}^{†n}+\hat{a}^n)$. When an $n$-photon-excitation resonance condition is satisfied, the presence of n photons in the cavity suppresses the absorption of the subsequent photons. To confirm the validity of this proposal, we study the n-photon blockade in an atom-cavity system, a Kerr-nonlinear resonator, and two-coupled Kerr nonlinear resonators. Our results demonstrate that $n$-photon bunching and $(n+1)$-photon antibunching can be simultaneously obtained in these systems. This effect is due both to the anharmonic energy ladder and to the nature of the $n$-photon drive. To show the importance of the drive, we compare the results of the $n$-photon drive with a coherent (one-photon) drive, proving the enhancement of antibunching in the parametric-drive case. This proposal is general and can be applied to realize the $n$-photon blockade in other nonlinear systems.

quant-ph↗

arXiv2023

Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems

Phase transitions in non-Hermitian systems are at the focus of cutting edge theoretical and experimental research. On the one hand, parity-time- ($\cal PT$-) and anti-$\cal PT$-symmetric physics have gained ever-growing interest, due to the existence of non-Hermitian spectral singularities called exceptional points (EPs). On the other, topological and localization transitions in non-Hermitian systems reveal new phenomena, e.g., the non-Hermitian skin effect and the absence of conventional bulk-boundary correspondence. The great majority of previous studies exclusively focus on non-Hermitian Hamiltonians, whose realization requires an {\it a priori} fine-tuned extended lattices to exhibit topological and localization transition phenomena.In this work, we show how the non-Hermitian localization phenomena can naturally emerge in the synthetic field moments space of zero-dimensional bosonic systems, e.g., in anti-$\cal PT$ and $\cal PT$-symmetric quantum dimers. This offers an opportunity to simulate localization transitions in low-dimensional systems, without the need to construct complex arrays of, e.g., coupled cavities or waveguides. Indeed, the field moment equations of motion can describe an equivalent (quasi-)particle moving in a one-dimensional (1D) synthetic lattice. This synthetic field moments space can exhibit a nontrivial localization phenomena, such as non-Hermitian skin effect, induced by the presence of highly-degenerate EPs. We demonstrate our findings on the example of an anti-$\cal PT$-symmetric two-mode system, whose higher-order field moments eigenspace is emulated by a synthetic 1D non-Hermitian Hamiltonian having a Sylvester matrix shape. Our results can be directly verified in state-of-the-art optical setups, such as superconducting circuits and toroidal resonators, by measuring photon moments or correlation functions.

quant-ph↗

arXiv2022

Quantum error correction using squeezed Schrödinger cat states

Bosonic quantum codes redundantly encode quantum information in the states of a quantum harmonic oscillator, making it possible to detect and correct errors. Schrödinger cat codes -- based on the superposition of two coherent states with opposite displacements -- can correct phase-flip errors induced by dephasing, but they are vulnerable to bit-flip errors induced by particle loss. Here, we develop a bosonic quantum code relying on squeezed cat states, i.e. cat states made of a linear superposition of displaced-squeezed states. Squeezed cat states allow to partially correct errors caused by particle loss, while at the same time improving the protection against dephasing. We present a comprehensive analysis of the squeezed cat code, including protocols for code generation and elementary quantum gates. We characterize the effect of both particle loss and dephasing and develop an optimal recovery protocol that is suitable to be implemented on currently available quantum hardware. We show that with moderate squeezing, and using typical parameters of state-of-the-art quantum hardware platforms, the squeezed cat code has a resilience to particle loss errors that significantly outperforms that of the conventional cat code.

quant-ph↗

arXiv2022

Creating and controlling exceptional points of non-Hermitian Hamiltonians via homodyne Lindbladian invariance

The Exceptional Points (EPs) of non-Hermitian Hamiltonians (NHHs) are spectral degeneracies associated with coalescing eigenvalues and eigenvectors which are associated with remarkable dynamical properties. These EPs can be generated experimentally in open quantum systems, evolving under a Lindblad equation, by postselecting on trajectories that present no quantum jumps, such that the dynamics is ruled by a NHH. Interestingly, changing the way the information used for postselection is collected leads to different unravelings, i.e., different set of trajectories which average to the same Lindblad equation, but are associated with a different NHH. Here, we exploit this mechanism to create and control EPs solely by changing the measurement we postselect on. Our scheme is based on a realistic homodyne reading of the emitted leaking photons with a weak-intensity laser (a process which we call $β$-dyne), which we show generates a tunable NHH, that can exhibit EPs even though the system does have any in the absence of the laser. We consider a few illustrative examples pointing the dramatic effects that different postselections can have on the spectral features of the NHH, paving the road towards engineering of EPs in simple quantum systems.

quant-ph↗

arXiv2022

Flattening the Curve with Einstein's Quantum Elevator: Hermitization of Non-Hermitian Hamiltonians via a Generalized Vielbein Formalism

The formalism for non-Hermitian quantum systems sometimes blurs the underlying physics. We present a systematic study of the vielbein-like formalism which transforms the Hilbert space bundles of non-Hermitian systems into the conventional ones, rendering the induced Hamiltonian to be Hermitian. In other words, any non-Hermitian Hamiltonian can be "transformed" into a Hermitian one without altering the physics. Thus we show how to find a reference frame (corresponding to Einstein's quantum elevator) in which a non-Hermitian system, equipped with a non-trivial Hilbert space metric, reduces to a Hermitian system within the standard formalism of quantum mechanics.

quant-ph↗

arXiv2022

Non-Gaussian superradiant transition via three-body ultrastrong coupling

We introduce a class of quantum optical Hamiltonian characterized by three-body couplings, and propose a circuit-QED scheme based on state-of-the-art technology that implements the considered model. Unlike two-body light-matter interactions, this three-body coupling Hamiltonian is exclusively composed of terms which do not conserve the particle number. We explore the three-body ultrastrong coupling regime, showing the emergence of a superradiant phase transition which is of first order, is characterized by the breaking of a $\mathbb{Z}_2\times \mathbb{Z}_2$ symmetry and has a strongly non-Gaussian nature. Indeed, in contrast to what is observed in any two-body-coupling model, in proximity of the transition the ground state exhibits a divergent coskewness, i.e., quantum correlations that cannot be captured within semiclassical and Gaussian approximations. Furthermore, we demonstrate the robustness of our findings by including dissipative processes in the model, showing that the steady-state of the system inherits from the ground states the most prominent features of the transition.

quant-ph↗

arXiv2022

Arnoldi-Lindblad time evolution: Faster-than-the-clock algorithm for the spectrum of time-independent and Floquet open quantum systems

The characterization of open quantum systems is a central and recurring problem for the development of quantum technologies. For time-independent systems, an (often unique) steady state describes the average physics once all the transient processes have faded out, but interesting quantum properties can emerge at intermediate timescales. Given a Lindblad master equation, these properties are encoded in the spectrum of the Liouvillian whose diagonalization, however, is a challenge even for small-size quantum systems. Here, we propose a new method to efficiently provide the Liouvillian spectral decomposition. We call this method an Arnoldi-Lindblad time evolution, because it exploits the algebraic properties of the Liouvillian superoperator to efficiently construct a basis for the Arnoldi iteration problem. The advantage of our method is double: (i) It provides a faster-than-the-clock method to efficiently obtain the steady state, meaning that it produces the steady state through time evolution shorter than needed for the system to reach stationarity. (ii) It retrieves the low-lying spectral properties of the Liouvillian with a minimal overhead, allowing to determine both which quantum properties emerge and for how long they can be observed in a system. This method is general and model-independent, and lends itself to the study of large systems where the determination of the Liouvillian spectrum can be numerically demanding but the time evolution of the density matrix is still doable. Our results can be extended to time evolution with a time-dependent Liouvillian. In particular, our method works for Floquet (i.e., periodically driven) systems, where it allows not only to construct the Floquet map for the slow-decaying processes, but also to retrieve the stroboscopic steady state and the eigenspectrum of the Floquet map. We apply our method to several examples.

quant-ph↗

arXiv2022

Continuous Dissipative Phase Transitions without Symmetry Breaking

The paradigm of second-order phase transitions (PTs) induced by spontaneous symmetry breaking (SSB) in thermal and quantum systems is a pillar of modern physics that has been fruitfully applied to out-of-equilibrium open quantum systems. Dissipative phase transitions (DPTs) of second order are often connected with SSB, in close analogy with well-known thermal second-order PTs in closed quantum and classical systems. That is, a second-order DPT should disappear by preventing the occurrence of SSB. Here, we prove this statement to be wrong, showing that, surprisingly, SSB is not a necessary condition for the occurrence of second-order DPTs in out-of-equilibrium open quantum systems. We analytically prove this result using the Liouvillian theory of dissipative phase transitions, and demonstrate this anomalous transition in a paradigmatic laser model, where we can arbitrarily remove SSB while retaining criticality, and on a $Z_2$-symmetric model of a two-photon Kerr resonator. This new type of phase transition cannot be interpreted as a "semiclassical" bifurcation, because, after the DPT, the system steady state remains unique.

quant-ph↗

arXiv2022

Liouvillian spectral collapse in the Scully-Lamb laser model

Phase transitions of thermal systems and the laser threshold were first connected more than forty years ago. Despite the nonequilibrium nature of the laser, the Landau theory of thermal phase transitions, applied directly to the Scully-Lamb laser model (SLLM), indicates that the laser threshold is a second-order phase transition, associated with a $U(1)$ spontaneous symmetry breaking (SSB). To capture the genuine nonequilibrium phase transition of the SLLM (i.e., a single-mode laser without a saturable absorber), here we employ a quantum theory of dissipative phase transitions. Our results confirm that the $U(1)$ SSB can occur at the lasing threshold but, in contrast to the Landau theory and semiclassical approximation, they signal that the SLLM "fundamental" transition is a different phenomenon, which we call Liouvillian spectral collapse; that is, the emergence of diabolic points of infinite degeneracy. By considering a generalized SLLM with additional dephasing, we witness a second-order phase transition, with a Liouvillian spectral collapse, but in the absence of symmetry breaking. Most surprisingly, the phase transition corresponds to the emergence of dynamical multistability even without SSB. Normally, bistability is suppressed by quantum fluctuations, while in this case, the very presence of quantum fluctuations enables bistability. This rather anomalous bistability, characterizing the truly dissipative and quantum origin of lasing, can be an experimental signature of our predictions, and we show that it is associated with an emergent dynamical hysteresis.

quant-ph↗

arXiv2021

Dispersive qubit readout with machine learning

Open quantum systems can undergo dissipative phase transitions, and their critical behavior can be exploited in sensing applications. For example, it can be used to enhance the fidelity of superconducting qubit readout measurements, a central problem toward the creation of reliable quantum hardware. A recently introduced measurement protocol, named ``critical parametric quantum sensing'', uses the parametric (two-photon driven) Kerr resonator's driven-dissipative phase transition to reach single-qubit detection fidelity of 99.9\% [arXiv:2107.04503]. In this work, we improve upon the previous protocol by using machine learning-based classification algorithms to \textit{efficiently and rapidly} extract information from this critical dynamics, which has so far been neglected to focus only on stationary properties. These classification algorithms are applied to the time series data of weak quantum measurements (homodyne detection) of a circuit-QED implementation of the Kerr resonator coupled to a superconducting qubit. This demonstrates how machine learning methods enable a faster and more reliable measurement protocol in critical open quantum systems.

quant-ph↗

arXiv2021

Quantum dynamics of Dissipative Kerr solitons

Dissipative Kerr solitons arising from parametric gain in ring microresonators are usually described within a classical mean-field framework. Here, we develop a quantum-mechanical model of dissipative Kerr solitons in terms of the truncated Wigner method, which accounts for quantum effects to lowest order. We show that the soliton experiences a finite lifetime due to quantum fluctuations originating from losses. Reading the results in terms of the theory of open quantum systems, allows to estimate the Liouvillian spectrum of the system. It is characterized by a set of eigenvalues with finite imaginary part and vanishing real part in the limit of vanishing quantum fluctuations. This feature shows that dissipative Kerr solitons are a specific class of dissipative time crystals.

quant-ph↗

arXiv2021

Generating high-order quantum exceptional points in synthetic dimensions

Recently, there has been intense research in proposing and developing various methods for constructing high-order exceptional points (EPs) in dissipative systems. These EPs can possess a number of intriguing properties related to, e.g., chiral transport and enhanced sensitivity. Previous proposals to realize non-Hermitian Hamiltonians (NHHs) with high-order EPs have been mainly based on either direct construction of spatial networks of coupled modes or utilization of synthetic dimensions, e.g., of mapping spatial lattices to time or photon-number space. Both methods rely on the construction of effective NHHs describing classical or postselected quantum fields, which neglect the effects of quantum jumps, and which, thus, suffer from a scalability problem in the {\it quantum regime}, when the probability of quantum jumps increases with the number of excitations and dissipation rate. Here, by considering the full quantum dynamics of a quadratic Liouvillian superoperator, we introduce a simple and effective method for engineering NHHs with high-order quantum EPs, derived from evolution matrices of system operators moments. That is, by quantizing higher-order moments of system operators, e.g., of a quadratic two-mode system, the resulting evolution matrices can be interpreted as alternative NHHs describing, e.g., a spatial lattice of coupled resonators, where spatial sites are represented by high-order field moments in the synthetic space of field moments. As an example, we consider a $U(1)$-symmetric quadratic Liouvillian describing a {\it bimodal} cavity with incoherent mode coupling, which can also possess anti-$\cal PT$-symmetry, whose field moment dynamics can be mapped to an NHH governing a spatial {\it network} of coupled resonators with high-order EPs.

quant-ph↗

arXiv2021

Dissipative state transfer and Maxwell's demon in single quantum trajectories: Excitation transfer between two noninteracting qubits via unbalanced dissipation rates

We introduce a protocol to transfer excitations between two noninteracting qubits via purely dissipative processes (i.e., in the Lindblad master equation there is no coherent interaction between the qubits). The fundamental ingredients are the presence of collective (i.e. nonlocal) dissipation and unbalanced local dissipation rates (the qubits dissipate at different rates). The resulting quantum trajectories show that the measurement backaction changes the system wave function and induces a passage of the excitation from one qubit to the other. While similar phenomena have been witnessed for a non-Markovian environment, here the dissipative quantum state transfer is induced by an update of the observer knowledge of the wave function in the presence of a Markovian (memoryless) environment -- this is a single quantum trajectory effect. Beyond single quantum trajectories and postselection, such an effect can be observed by histogramming the quantum jumps along several realizations at different times. By investigating the effect of the temperature in the presence of unbalanced local dissipation, we demonstrate that, if appropriately switched on and off, the collective dissipator can act as a Maxwell's demon. These effects are a generalized measure equivalent to the standard projective measure description of quantum teleportation and Maxwell's demon. They can be witnessed in state-of-the-art setups given the extreme experimental control in, e.g., superconducting qubits or Rydberg atoms.

quant-ph↗

arXiv2020

Liouvillian exceptional points of any order in dissipative linear bosonic systems: Coherence functions and switching between ${\cal PT}$ and anti-${\cal PT}$ symmetries

Usually, when investigating exceptional points (EPs) of an open Markovian bosonic system, one deals with spectral degeneracies of a non-Hermitian Hamiltonian (NHH), which can correctly describe the system dynamics only in the semiclassical regime. A recently proposed quantum Liouvillian framework enables to completely determine the dynamical properties of such systems and their EPs (referred to as Liouvillian EPs, or LEPs) in the quantum regime by taking into account the effects of quantum jumps, which are ignored in the NHH formalism. Moreover, the symmetry and eigenfrequency spectrum of the NHH become a part of much larger Liouvillian eigenspace. As such, the EPs of an NHH form a subspace of the LEPs. Here we show that once an NHH of a dissipative linear bosonic system exhibits an EP of a certain finite order $n$, it immediately implies that the corresponding LEP can become of any higher order $m\geq n$, defined in the infinite Hilbert space. Most importantly, these higher-order LEPs can be identified by the coherence and spectral functions at the steady state. The coherence functions can offer a convenient tool to probe extreme system sensitivity to external perturbations in the vicinity of higher-order LEPs. As an example, we study a linear bosonic system of a bimodal cavity with incoherent mode coupling to reveal its higher-order LEPs; particularly, of second and third order via first- and second-order coherence functions, respectively. Accordingly, these LEPs can be additionally revealed by squared and cubic Lorentzian spectral lineshapes in the power and intensity-fluctuation spectra. Moreover, we demonstrate that these EPs can also be associated with spontaneous parity-time (${\cal PT}$) and anti-${\cal PT}$-symmetry breaking in the system studied.

quant-ph↗

arXiv2020

Correspondence between dissipative phase transitions of light and time crystals

We predict the emergence of a time crystal generated by an incoherently driven and dissipative nonlinear optical oscillator, where the nonlinearity also comes from dissipation. We show that a second-order dissipative phase transition of light occurs in the frame rotating at the cavity frequency, while a boundary (dissipative) time crystal emerges in the laboratory frame. We relate these two phenomena by using the Liouvillian superoperator associated with the Lindblad master equation and its symmetries. These results connect the emergence of a second-order dissipative phase transition and a dissipative time crystal in the thermodynamic limit, allowing to interpret them as the same phenomenon in terms of the Liouvillian spectrum, but just in different frames.

quant-ph↗