As recently manifested 1, 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 the non-interacting 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.
Abstract
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 accompany superabsorption. This engineered separation of processes greatly improves the efficiency and the scalability of the system.
Nanotubular molecular self-aggregates are characterized by a high degree of symmetry and they are fundamental systems for light-harvesting and energy transport. While coherent effects are thought to ...be at the basis of their high efficiency, the relationship between structure, coherence and functionality is still an open problem. We analyse natural nanotubes present in Green Sulphur Bacteria. We show that they have the ability to support macroscopic coherent states, i.e. delocalized excitonic states coherently spread over many molecules, even at room temperature. Specifically, assuming a canonical thermal state we find, in natural structures, a large thermal coherence length, of the order of 1000 molecules. By comparing natural structures with other mathematical models, we show that this macroscopic coherence cannot be explained either by the magnitude of the nearest-neighbour coupling between the molecules, which would induce a thermal coherence length of the order of 10 molecules, nor by the presence of long-range interactions between the molecules. Indeed we prove that the existence of macroscopic coherent states is an emergent property of such structures due to the interplay between geometry and cooperativity (superradiance and super-transfer). In order to prove that, we give evidence that the lowest part of the spectrum of natural systems is determined by a cooperatively enhanced coupling (super-transfer) between the eigenstates of modular sub-units of the whole structure. Due to this enhanced coupling strength, the density of states is lowered close to the ground state, thus boosting the thermal coherence length. As a striking consequence of the lower density of states, an energy gap between the excitonic ground state and the first excited state emerges. Such energy gap increases with the length of the nanotube (instead of decreasing as one would expect), up to a critical system size which is close to the length of the natural complexes considered.
A comparison between the single particle spectrum of the discrete Bardeen-Cooper-Schrieffer (BCS) model, used for small superconducting grains, and the spectrum of a paradigmatic model of Single ...Excitation Superradiance (SES) is presented. They are both characterized by an equally spaced energy spectrum (Picket Fence) where all the levels are coupled between each other by a constant coupling which is real for the BCS model and purely imaginary for the SES model. While the former corresponds to the discrete BCS-model describing the coupling of Cooper pairs in momentum space and it induces a Superconductive regime, the latter describes the coupling of single particle energy levels to a common decay channel and it induces a Superradiant transition. We show that the transition to a Superradiant regime can be connected to the emergence of an imaginary energy gap, similarly to the transition to a Superconductive regime where a real energy gap emerges. Despite their different physical origin, it is possible to show that both the Superradiant and the Superconducting gaps have the same magnitude in the large gap limit. Nevertheless, some differences appear: while the critical coupling at which the Superradiant gap appears is independent of the system size
N
, for the Superconductivity gap it scales as (ln
N
)
−1
, which is the expected BCS result. The presence of a gap in the imaginary energy axis between the Superradiant and the Subradiant states shares many similarities with the “standard” gap on the real energy axis: the superradiant state is protected against disorder from the imaginary gap as well as the superconducting ground state is protected by the real energy gap. Moreover we connect the origin of the gapped phase to the long-range nature of the coupling between the energy levels.
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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/sqrtN, respectively, for weak and moderate static disorder. When focusing on the excitation starting at the beginning of the chain, dephasing can help excitation transfer only above a critical value of disorder W^{cr}, which strongly depends on the sink coupling strength Γ_{trap}. Analytic solutions are obtained for short chains.
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In recent experiments with ion traps, long-range interactions were associated with the exceptionally fast propagation of perturbation, while in some theoretical works they have also been related with ...the suppression of propagation. Here, we show that such apparently contradictory behavior is caused by a general property of long-range interacting systems, which we name cooperative shielding. It refers to shielded subspaces that emerge as the system size increases and inside of which the evolution is unaffected by long-range interactions for a long time. As a result, the dynamics strongly depends on the initial state: if it belongs to a shielded subspace, the spreading of perturbation satisfies the Lieb-Robinson bound and may even be suppressed, while for initial states with components in various subspaces, the propagation may be quasi-instantaneous. We establish an analogy between the shielding effect and the onset of quantum Zeno subspaces. The derived effective Zeno Hamiltonian successfully describes the short-ranged dynamics inside the subspaces up to a time scale that increases with system size. Cooperative shielding can be tested in current experiments with trapped ions.
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Magnetic resonance force microscopy (MRFM) is a rapidly evolving field which originated in 1990s and matured recently with the first detection of a single electron spin below the surface of a ...non-transparent solid. Further development of MRFM techniques will have a great impact on many areas of science and technology including physics, chemistry, biology, and even medicine. Scientists, engineers, and students from various backgrounds will all be interested in this promising field. The objective of this “multi-level” book is to describe the basic principles, applications, and the advanced theory of MRFM. Focusing on the experimental oscillating cantilever-driven adiabatic reversals (OSCAR) detection technique for single electron spin, this book contains valuable research data for scientists working in the field of quantum physics or magnetic resonance. Readers unfamiliar with quantum mechanics and magnetic resonance will be able to obtain an understanding and appreciation of the basic principles of MRFM.
Overcoming the detrimental effect of disorder at the nanoscale is very hard since disorder induces localization and an exponential suppression of transport efficiency. Here we unveil novel and robust ...quantum transport regimes achievable in nanosystems by exploiting long-range hopping. We demonstrate that in a 1D disordered nanostructure in the presence of long-range hopping, transport efficiency, after decreasing exponentially with disorder at first, is then enhanced by disorder disorder-enhanced transport (DET) regime until, counterintuitively, it reaches a disorder-independent transport (DIT) regime, persisting over several orders of disorder magnitude in realistic systems. To enlighten the relevance of our results, we demonstrate that an ensemble of emitters in a cavity can be described by an effective long-range Hamiltonian. The specific case of a disordered molecular wire placed in an optical cavity is discussed, showing that the DIT and DET regimes can be reached with state-of-the-art experimental setups.
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We analyze a one-dimensional 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.
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