Papers by fausto borgonovi
arXiv (Cornell University), Mar 3, 2001
Recently, the question of a relevance of quantum chaos has been discussed in applications to quan... more Recently, the question of a relevance of quantum chaos has been discussed in applications to quantum computation . Indeed, according to the general approach to closed systems of finite number of interacting Fermi-particles (see, e.g. ), as the interaction between quibits increases a kind of chaos is expected to emerge in the energy spectra and structure of many-body states. Specifically, the fluctuations of energy levels and components of the eigenstates turn out to be very large and they are described by the random matrix theory. Clearly, if this happens in a quantum computer, it may lead to a destruction of the coherence (due to an internal decoherence inside many-body states) required for quantum computations. It is important to stress that the quantum chaos occurs not only in the systems with random interactions, but also for purely dynamical interactions. In the latter case, the mechanism of chaos is the non-linear two-body interaction represented in the basis of non-interacting particles. Numerical analysis [1] of the simplest model of a quantum computer (2D model of 1/2-spins with a random interqubit interaction J) shows that as the number, L, of qubits increases, the chaos threshold J cr decreases as J cr ∝ 1/L. Consequently, it was claimed that the onset of quantum chaos is a real danger for the quantum computers with large L ≫ 1. On the other hand, in [2] is was argued that in order to treat this problem properly, one needs to distinguish between the chaotic properties of stationary states and the dynamical process of quantum computation. Below, we report our theoretical and numerical results for a realistic model of quantum computer, described in . We consider both stationary and
arXiv (Cornell University), Aug 7, 2015
Disordered quantum networks, as those describing light-harvesting complexes, are often characteri... more Disordered quantum networks, as those describing light-harvesting complexes, are often characterized by the presence of antenna structures where the light is captured and inner structures (reaction centers) where the excitation is transferred. Antennae often display distinguished coherent features: their eigenstates can be separated, with respect to the transfer of excitation, in the two classes of superradiant and subradiant states. Both are important to optimize transfer efficiency. In absence of disorder superradiant states have an enhanced coupling strength to the RC, while subradiant ones are basically decoupled from it. Disorder induces a coupling between subradiant and superradiant states, thus creating an indirect coupling to the RC. We consider the problem of finding the maximal excitation transfer efficiency as a function of the RC energy and the disorder strength, first in a paradigmatic threelevel system and then in a realistic model for the light-harvesting complex of purple bacteria. Specifically, we focus on the case in which the excitation is initially on a subradiant state, showing that the optimal disorder is of the order of the superradiant coupling. We also determine the optimal detuning between the initial state and the RC energy. We show that the efficiency remains high around the optimal detuning in a large energy window, proportional to the superradiant coupling. This allows for the simultaneous optimization of excitation transfer from several initial states with different optimal detuning.
arXiv (Cornell University), Feb 22, 2018
We demonstrate analytically and numerically that in isolated quantum systems of many interacting ... more We demonstrate analytically and numerically that in isolated quantum systems of many interacting particles, the number of many-body states participating in the evolution after a quench increases exponentially in time, provided the eigenstates are delocalized in the energy shell. The rate of the exponential growth is defined by the width Γ of the local density of states (LDOS) and is associated with the Kolmogorov-Sinai entropy for systems with a well defined classical limit. In a finite system, the exponential growth eventually saturates due to the finite volume of the energy shell. We estimate the time scale for the saturation and show that it is much larger than h/Γ. Numerical data obtained for a two-body random interaction model of bosons and for a dynamical model of interacting spin-1/2 particles show excellent agreement with the analytical predictions.
arXiv (Cornell University), Jul 11, 2023
Static disorder in a 3D crystal degrades the ideal ballistic dynamics until it produces a localiz... more Static disorder in a 3D crystal degrades the ideal ballistic dynamics until it produces a localized regime. This Metal-Insulator Transition is often preceded by coherent diffusion. By studying three different paradigmatic 1D models, the Harper-Hofstadter-Aubry-André and the Fibonacci tightbinding chains, and the power-banded random matrix model, we show that whenever coherent diffusion is present, transport is exceptionally stable against decoherent noise. This is completely at odds with what happens for ballistic and localized dynamics, where the diffusion coefficient strongly depends on the environmental decoherence. A universal dependence of the diffusion coefficient on the decoherence strength is analytically derived: the diffusion coefficient remains almost decoherenceindependent until the coherence time becomes comparable with the mean elastic scattering time. Thus, systems with a quantum diffusive regime could be used to design stable quantum wires and may explain the functionality of many biological systems, which often operate at the border between the ballistic and localized regimes.
Physical Review E, 2021
We address the old and widely debated question of the statistical properties of integrable quantu... more We address the old and widely debated question of the statistical properties of integrable quantum systems, through the analysis of the paradigmatic Lieb-Liniger model. This quantum many-body model of 1-d interacting bosons allows for the rigorous determination of energy spectra via the Bethe ansatz approach and our interest is understanding whether Poisson statistics is a characteristic feature of this model. Using both analytical and numerical studies we show that the properties of spectra strongly depend on whether the analysis is done for a full energy spectrum or for a single subset with fixed total momentum. We show that the Poisson distribution of spacing between nearest-neighbor energies can occur only for a set of energy levels with fixed total momentum, for neither too large nor too weak interaction strength, and for sufficiently high energy. On the other hand, when studying long-range correlations between energy levels, we found strong deviations from the predictions given by a Poisson process.
New Journal of Physics, 2022
Efficient devices for light harvesting and photon sensing are fundamental building blocks of basi... more Efficient devices for light harvesting and photon sensing are fundamental building blocks of basic energy science and many essential technologies. Recent efforts have turned to biomimicry to design the next generation of light-capturing devices, partially fueled by an appreciation of the fantastic efficiency of the initial stages of natural photosynthetic systems at capturing photons. In such systems extended excitonic states are thought to play a fundamental functional role, inducing cooperative coherent effects, such as superabsorption of light and supertransfer of photoexcitations. Inspired by this observation, we design an artificial light-harvesting and photodetection device that maximally harnesses cooperative effects to enhance efficiency. The design relies on separating absorption and transfer processes (energetically and spatially) in order to overcome the fundamental obstacle to exploiting cooperative effects to enhance light capture: the enhanced emission processes that a...
arXiv: Mesoscale and Nanoscale Physics, 2015
Disordered quantum networks, as those describing light-harvesting complexes, are often characteri... more Disordered quantum networks, as those describing light-harvesting complexes, are often characterized by the presence of antenna structures where the light is captured and inner structures (reaction centers) where the excitation is transferred. Antennae often display distinguished coherent features: their eigenstates can be separated, with respect to the transfer of excitation, in the two classes of superradiant and subradiant states. Both are important to optimize transfer efficiency. In absence of disorder superradiant states have an enhanced coupling strength to the RC, while subradiant ones are basically decoupled from it. Disorder induces a coupling between subradiant and superradiant states, thus creating an indirect coupling to the RC. We consider the problem of finding the maximal excitation transfer efficiency as a function of the RC energy and the disorder strength, first in a paradigmatic three-level system and then in a realistic model for the light-harvesting complex of ...
Quantum Information and Computation, 2004
We simulated the quantum dynamics for magnetic resonance force microscopy (MRFM) in the oscillati... more We simulated the quantum dynamics for magnetic resonance force microscopy (MRFM) in the oscillating cantilever-driven adiabatic reversals (OSCAR) technique. We estimated the frequency shift of the cantilever vibrations and demonstrated that this shift causes the formation of a Schr\"odinger cat state which has some similarities and differences from the conventional MRFM technique which uses cyclic adiabatic reversals of spins. The interaction of the cantilever with the environment is shown to quickly destroy the coherence between the two possible cantilever trajectories. We have shown that using partial adiabatic reversals, one can produce a significant increase in the OSCAR signal.
New Journal of Physics, 2020
As recently manifested , the quench dynamics of isolated quantum systems consisting of a finite n... more As recently manifested , the quench dynamics of isolated quantum systems consisting of a finite number of particles, is characterized by an exponential spreading of wave packets in the many-body Hilbert space. This happens when the inter-particle interaction is strong enough, thus resulting in a chaotic structure of the many-body eigenstates considered in an unperturbed basis. The semi-analytical approach used here, allows one to estimate the rate of the exponential growth as well as the relaxation time, after which the equilibration (thermalization) emerges. The key ingredient parameter in the description of this process is the width Γ of the Local Density of States (LDoS) defined by the initially excited state, the number of particles and the interaction strength. In this paper we show that apart from the meaning of Γ as the decay rate of survival probability, the width of the LDoS is directly related to the diagonal entropy and the latter can be linked to the thermodynamic entropy of a system equilibrium state emerging after the complete relaxation. The analytical expression relating the two entropies is derived phenomenologically and numerically confirmed in a model of bosons with random two-body interaction, as well as in a deterministic model which becomes completely integrable in the continuous limit.
We study, under very general conditions and in a variety of geometries, quantum enhancement of tr... more We study, under very general conditions and in a variety of geometries, quantum enhancement of transport in open systems. Both static disorder and dephasing associated with dynamical disorder (or finite temperature) are fully included in the analysis. We show that quantum coherence effects may significantly enhance transport in open quantum systems even in the semiclassical regime (where the decoherence rate is greater than the inter-site hopping amplitude), as long as the static disorder is sufficiently strong. When the strengths of static and dynamical disorder are fixed, there is an optimal opening strength at which the coherent transport enhancement is optimized. Analytic results are obtained in two simple paradigmatic tight-binding models of large systems: the linear chain and the fully connected network. The physical behavior is also reflected, for example, in the FMO photosynthetic complex, which may be viewed as being intermediate between these paradigmatic models. We furthermore show that a nonzero dephasing rate assists transport in an open linear chain when the disorder strength exceeds a critical value, and obtain this critical disorder strength as a function of the degree of opening.
Physical review. E, 2017
We study the interplay between dephasing, disorder, and coupling to a sink on transport efficienc... more We study the interplay between dephasing, disorder, and coupling to a sink on transport efficiency in a one-dimensional chain of finite length N, and in particular the beneficial or detrimental effect of dephasing on transport. The excitation moves along the chain by coherent nearest-neighbor hopping Ω, under the action of static disorder W and dephasing γ. The last site is coupled to an external acceptor system (sink), where the excitation can be trapped with a rate Γ_{trap}. While it is known that dephasing can help transport in the localized regime, here we show that dephasing can enhance energy transfer even in the ballistic regime. Specifically, in the localized regime we recover previous results, where the optimal dephasing is independent of the chain length and proportional to W or W^{2}/Ω. In the ballistic regime, the optimal dephasing decreases as 1/N or 1/sqrt[N], respectively, for weak and moderate static disorder. When focusing on the excitation starting at the beginning...
Physical Review B, 2016
We investigate a paradigmatic model for quantum transport with both nearest-neighbor and infinite... more We investigate a paradigmatic model for quantum transport with both nearest-neighbor and infinite range hopping coupling (independent of the position). Due to long range homogeneous hopping, a gap between the ground state and the excited states can be induced, which is mathematically equivalent to the superconducting gap. In the gapped regime, the dynamics within the excited states subspace is shielded from long range hopping, namely it occurs as if long range hopping would be absent. This is a cooperative phenomenon since shielding is effective over a time scale which diverges with the system size. We named this effect Cooperative Shielding. We also discuss the consequences of our findings on Anderson localization. Long range hopping is usually thought to destroy localization due to the fact that it induces an infinite number of resonances. Contrary to this common lore we show that the excited states display strong localized features when shielding is effective even in the regime of strong long range coupling. A brief discussion on the extension of our results to generic power-law decaying long range hopping is also given. Our preliminary results confirms that the effects found for the infinite range case are generic.
Physical Review E, 2016
Disordered quantum networks, as those describing light-harvesting complexes, are often characteri... more Disordered quantum networks, as those describing light-harvesting complexes, are often characterized by the presence of peripheral ring-like structures, where the excitation is initialized, and inner structures, reaction centers (RC), where the excitation is trapped and transferred. The peripheral rings often display distinguished coherent features: their eigenstates can be separated, with respect to the transfer of excitation, in the two classes of superradiant and subradiant states. Both are important to optimize transfer efficiency. In the absence of disorder, superradiant states have an enhanced coupling strength to the RC, while the subradiant ones are basically decoupled from it. Static on-site disorder induces a coupling between subradiant and superradiant states, thus creating an indirect coupling to the RC. The problem of finding the optimal transfer conditions, as a function of both the RC energy and the disorder strength, is very complex even in the simplest network, namely a three-level system. In this paper we analyze such trimeric structure choosing as initial condition an excitation on a subradiant state, rather than the more common choice of an excitation localized on a single site. We show that, while the optimal disorder is of the order of the superradiant coupling, the optimal detuning between the initial state and the RC energy strongly depends on system parameters: when the superradiant coupling is much larger than the energy gap between the superradiant and the subradiant levels, optimal transfer occurs if the RC energy is at resonance with the subradiant initial state, whereas we find an optimal RC energy at resonance with a virtual dressed state when the superradiant coupling is smaller than or comparable with the gap. The presence of dynamical noise, which induces dephasing and decoherence, affects the resonance structure of energy transfer producing an additional "incoherent" resonance peak, which corresponds to the RC energy being equal to the energy of the superradiant state.
Physical Review E, 2001
We study the properties of spectra and eigenfunctions for a chain of 1/2-spins (qubits) in an ext... more We study the properties of spectra and eigenfunctions for a chain of 1/2-spins (qubits) in an external time-dependent magnetic field, and under the conditions of non-selective excitation (when the amplitude of the magnetic field is large). This model is known as a possible candidate for experimental realization of quantum computation. We present the theory for finding delocalization transition and show that for the interaction between nearest qubits, the transition is very different from that to quantum chaos. We explain this phenomena by showing that in the considered region of parameters our model is close to an integrable one. According to a general opinion, the threshold for the onset of quantum chaos due to the interqubit interaction decreases with an increase of the number of qubits. Contrary to this expectation, for a magnetic field with constant gradient we have found that chaos border does not depend on the number of qubits. We give analytical estimates which explain this effect, together with numerical data supporting our analysis. Random models with long-range interactions are studied as well. In particular, we show that in this case the delocalization and quantum chaos borders coincide.
Physical Review E, 2000
We study the emergence of Boltzmann's law for the "single particle energy distribution" in a clos... more We study the emergence of Boltzmann's law for the "single particle energy distribution" in a closed system of interacting classical spins. It is shown that for a large number of particles Boltzmann's law may occur, even if the interaction is very strong. Specific attention is paid to classical analogs of the average shape of quantum eigenstates and "local density of states", which are very important in quantum chaology. Analytical predictions are then compared with numerical data.
We analyze a 1-d ring structure composed of many two-level systems, in the limit where only one e... more We analyze a 1-d ring structure composed of many two-level systems, in the limit where only one excitation is present. The two-level systems are coupled to a common environment, where the excitation can be lost, which induces super and subradiant behavior, an example of cooperative quantum coherent effect. We consider time-independent random fluctuations of the excitation energies. This static disorder, also called inhomogeneous broadening in literature, induces Anderson localization and is able to quench Superradiance. We identify two different regimes: i) weak opening, in which Superradiance is quenched at the same critical disorder at which the states of the closed system localize; ii) strong opening, with a critical disorder strength proportional to both the system size and the degree of opening, displaying robustness of cooperativity to disorder. Relevance to photosynthetic complexes is discussed.
Physical Review B, 2014
We analyze a 1-d ring structure composed of many two-level systems, in the limit where only one e... more We analyze a 1-d ring structure composed of many two-level systems, in the limit where only one excitation is present. The two-level systems are coupled to a common environment, where the excitation can be lost, which induces super and subradiant behavior, an example of cooperative quantum coherent effect. We consider time-independent random fluctuations of the excitation energies. This static disorder, also called inhomogeneous broadening in literature, induces Anderson localization and is able to quench Superradiance. We identify two different regimes: i) weak opening, in which Superradiance is quenched at the same critical disorder at which the states of the closed system localize; ii) strong opening, with a critical disorder strength proportional to both the system size and the degree of opening, displaying robustness of cooperativity to disorder. Relevance to photosynthetic complexes is discussed.
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2002
We study a one-dimensional chain of nuclear 1/2-spins in an external time-dependent magnetic fiel... more We study a one-dimensional chain of nuclear 1/2-spins in an external time-dependent magnetic field. This model is considered as a possible candidate for experimental realization of quantum computation. According to general theory of interacting particles, one of the most dangerous effects is quantum chaos which can destroy the stability of quantum operations. The standard viewpoint is that the threshold for the onset of quantum chaos due to an interaction between spins (qubits) strongly decreases with an increase of the number of qubits. Contrary to this opinion, we show that the presence of a non-homogeneous magnetic field can strongly reduce quantum chaos effects. We give analytical estimates which explain this effect, together with numerical data supporting our analysis.
The Journal of Physical Chemistry C, 2012
We investigate the role of long-lasting quantum coherence in the efficiency of energy transport a... more We investigate the role of long-lasting quantum coherence in the efficiency of energy transport at room temperature in Fenna-Matthews-Olson photosynthetic complexes. The excitation energy transfer due to coupling of the lightharvesting complex to the reaction center ("sink") is analyzed using an effective non-Hermitian Hamiltonian. We show that, as the coupling to the reaction center is varied, maximal efficiency in energy transport is achieved in the vicinity of the superradiance transition, characterized by a segregation of the imaginary parts of the eigenvalues of the effective non-Hermitian Hamiltonian. Our results demonstrate that the presence of the sink (which provides a quasi-continuum in the energy spectrum) is the dominant effect in the energy transfer which takes place even in the absence of a thermal bath. This approach allows one to study the effects of finite temperature and the effects of any coupling scheme to the reaction center. Moreover, taking into account a realistic electric dipole interaction, we show that the optimal distance from the reaction center to the Fenna-Matthews-Olson system occurs at the superradiance transition, and we show that this is consistent with available experimental data.
Physics Letters A, 2005
We propose a simple model which describes the statistical properties of quantum jumps in a single... more We propose a simple model which describes the statistical properties of quantum jumps in a singlespin measurement using the oscillating cantilever-driven adiabatic reversals technique in magnetic resonance force microscopy. Our computer simulations based on this model predict the average time interval between two consecutive quantum jumps and the correlation time to be proportional to the characteristic time of the magnetic noise and inversely proportional to the square of the magnetic noise amplitude.
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Papers by fausto borgonovi