A simplified Heisenberg spin model is studied in order to examine the idea of decoherence in closed quantum systems. For this purpose, we present a quantifiable definition to quantum coherence $Ξ$, and discuss in some detail a general coherence theory and its elementary results. As expected, decoherence is understood as a statistical process that is caused by the dynamics of the system, similar to the growth of entropy. It appears that coherence is an important measure that helps to understand quantum properties of a system, e.g., the decoherence time can be derived from the coherence function $Ξ(t)$, but not from the entropy dynamics. Moreover, the concept of decoherence time is applicable in closed and finite systems. However, in most cases, the decay of off-diagonal elements differs from the usual $\exp(-t/τ_{\rm d})$ behaviour. For concreteness, we report the form of decoherence time $τ_{\rm d}$ in a finite Heisenberg model with respect to the number of particles $N$, density $n_ρ$, spatial dimension $D$ and $ε$ in a $η/r^ε$-type of potential.
A theoretical description in terms of the coherence propagation is given for self-focussing. The concept of coherence length is defined in terms of free, self-focussing propagation giving results in accordance with well known experimental criteria for the laser. Extension of the method is given for an Atom Laser showing good results in agreement with recents numerical results of Trippenbach et. al.: J. Phys. B:At. Mol. Opt. Phys. 33, 47-54 (2000).
We theoretically and experimentally demonstrate coherence phenomena in optical parametric amplification inside a cavity. The mode splitting in transmission spectra of phase-sensitive optical parametric amplifier is observed. Especially, we show a very narrow dip and peak, which are the shape of $δ$ function, appear in the transmission profile. The origin of the coherence phenomenon in this system is the interference between the harmonic pump field and the subharmonic seed field in cooperation with dissipation of the cavity.
We introduce unitary quantum gates for photon pair creation in spontaneous parametric down-conversion nonlinear crystals (NLs) and for photon path alignment. These are the two key ingredients for the method of "induced coherence without induced emission" and many ensuing variations thereof. The difficulty in doing so stems from an apparent mixing of the mode picture (such as the polarization of photons) and the Fock picture (such as the existence of the photons). We illustrate utility of these gates by obtaining quantum circuits for the experimental setups of the frustrated generation of photo…
The main aim of this article is to discuss characteristic physical phenomena which govern the destruction of quantum coherence of material wave packets.
Quantifying of quantum coherence of a given system not only plays an important role in quantum information science but also promote our understanding on some basic problems, such as quantum phase transition. Conventional quantum coherence measurements, such as $l_1$ norm of coherence and relative entropy of coherence, has been widely used to study quantum phase transition, which usually are basis-dependent. The recent quantum version of the Jensen-Shannon divergence meet all the requirements of a good coherence measure. It is not only a metric but also can be basis-independent. Here, based on …
Interference effects in quantum transitions, giving rise to amplification without inversion, optical transparency and to enhancements in nonlinear optical frequency conversions are considered. Review of the relevant early theoretical and experimental results is given. The role of relaxation processes, spontaneous cascade of polarizations, local field effects, Doppler-broadening, as well as specific features of the interference in the spectral continuum are discussed.
Superconducting qubits are a promising platform for building a larger-scale quantum processor capable of solving otherwise intractable problems. In order for the processor to reach practical viability, the gate errors need to be further suppressed and remain stable for extended periods of time. With recent advances in qubit control, both single- and two-qubit gate fidelities are now in many cases limited by the coherence times of the qubits. Here we experimentally employ closed-loop feedback to stabilize the frequency fluctuations of a superconducting transmon qubit, thereby increasing its coh…
We study the role of coherence in closed and open quantum batteries. We obtain upper bounds to the work performed or energy exchanged by both closed and open quantum batteries in terms of coherence. Specifically, we show that the energy storage can be bounded by the Hilbert-Schmidt coherence of the density matrix in the spectral basis of the unitary operator that encodes the evolution of the battery. We also show that an analogous bound can be obtained in terms of the battery's Hamiltonian coherence in the basis of the unitary operator by evaluating their commutator. We apply these bounds to a…
In artificial systems, quantum superposition and entanglement typically decay rapidly unless cryogenic temperatures are used. Could life have evolved to exploit such delicate phenomena? Certain migratory birds have the ability to sense very subtle variations in Earth's magnetic field. Here we apply quantum information theory and the widely accepted "radical pair" model to analyze recent experimental observations of the avian compass. We find that superposition and entanglement are sustained in this living system for at least tens of microseconds, exceeding the durations achieved in the best co…
The diagonal representation and optical equivalence theorem are the E. C. G. Sudarshan's mid 20th century adventures in non-classical optics. It basically deals with a quantum mechanical description of photons to explain the quantum properties of light. Inspired by Sudarshan's pioneering work we try to explain the every minute mathematical details of his paper "Equivalence of semi-classical and quantum mechanical descriptions of statistical light beams". In this article we are going to go through some of the basics in developing quantum optics, then land up in E.C.G's original work and try to …
Coherence, being at the heart of interference phenomena, is found to be an useful resource in quantum information theory. Here we want to understand quantum coherence under the combination of two fundamentally dual processes, viz., cloning and deleting. We found the role of quantum cloning and deletion machines with the consumption and generation of quantum coherence. We establish cloning as a cohering process and deletion as a decohering process. Fidelity of the process will be shown to have connection with coherence generation and consumption of the processes.
A symmetric four-level closed-loop $\diamondsuit$ type (the diamond structure) atomic system driven by four coherent optical fields is investigated. The system shows rich quantum interference and coherence features. When symmetry of the system is broken, interesting phenomena such as single and double dark resonances appear. As a result, the double electromagnetically induced transparency effect is generated, which will facilitate the implementation of quantum phase gate operation.
Developing an analytical theory for atomic coherence driven by ultrashort laster pulses has proved to be challenging due to the breakdown of the rotating wave approximation (RWA). In this paper, we present an approximate, closed-form solution to the Schrodinger equation that describes a two-level atom under the excitation of a far-off-resonance, few-cycle pulse of arbitrary shape without invoking the RWA. As an example of its applicability, an analytical solution for Gaussian pulses is explicitly given. Comparisons with numerical solutions validate the accuracy our solution within the scope of…
Using the axiomatic definition of the coherence measure, such as the $l_{1}$ norm and the relative entropy, we study the phenomena of two-qubit system quantum coherence through quantum channels where successive uses of the channels are memory. Different types of noisy channels with memory, such as amplitude damping, phase-damping, and depolarizing channels effect on quantum coherence have been discussed in detail. The results show that, quantum channels with memory can efficiently protect coherence from noisy channels. Particularly, as channels with perfect memory, quantum coherence is unaffec…
We discuss the effect of correlated noise on the robustness of quantum coherent phenomena. First we consider a simple, toy model to illustrate the effect of such correlations on the decoherence process. Then we show how decoherence rates can be suppressed using a Parrondo-like effect. Finally, we report the results of many-body calculations in which an experimentally-measurable quantum coherence phenomenon is significantly enhanced by non-Markovian dynamics arising from the noise source.
With the purpose to reveal consistency between multiple quantum (MQ) coherences and entanglement, we investigate numerically the dynamics of these phenomena in one-dimensional linear chains and ring of nuclear spins 1/2 coupled by dipole dipole interactions. As opposed to the calculation of the MQ coherence intensity based on the density matrix describing the spin system as a whole, we consider the "differentiated" intensity related only to the chosen spin pair based on the reduced density matrix. It is shown that the entanglement and the MQ coherence have similar dynamics only for nearest nei…
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state. Conversely, quantum phenomena are certified in terms of signed distributions, i.e., quasiprobabilities, and a residual component unaccessible via classical states. Our unifying method combines well-established concepts, such as phase-space distributions in quantum optics, with resources of quantumness relevant for quantum technologies. We apply our approach to …
We study the quasiprobability representation of quantum light, as introduced by Glauber and Sudarshan, for the unified characterization of quantum phenomena. We begin with reviewing the past and current impact of this technique. Regularization and convolution methods are specifically considered since they are accessible in experiments. We further discuss more general quantum systems for which the concept of negative probabilities can be generalized, being highly relevant for quantum information science. For analyzing quantum superpositions, we apply recently developed approaches to visualize q…
Quantum resource theories provide a diverse and powerful framework for extensively studying the phenomena in quantum physics. Quantum coherence, a quantum resource, is the basic ingredient in many quantum information tasks. It is a subject of broad and current interest in quantum information, and many new concepts have been introduced and generalized since its establishment. Here we show that the block coherence can be transformed into entanglement via a block incoherent operation. Moreover, we find that the POVM-based coherence associated with block coherence through the Naimark extension act…
Quantum devices are systems that can explore quantum phenomena, like entanglement or coherence, for example, to provide some enhancement performance concerning their classical counterparts. In particular, quantum batteries are devices that use entanglement as main element in its high performance in the charging powerful. In this paper, we explore the quantum battery performance and its relationship with the amount of entanglement that arises during the charging process. By using a general approach to a two and three-cell battery, our results suggest that entanglement is not the main resource t…
Quantum coherence is one of the most intriguing applications of quantum mechanics, and has led to interesting phenomena and uncommon results. Here we show that in a stark contrast to the usual red-detuned condition to observe bistability in single-mode optomechanics, the optical intensities exhibit bistability for all values of cavity-laser detuning due to intermode coupling induced by the two-photon coherence. Interestingly, an unconventional bistability with "ribbon"-shaped hysteresis can be observed for blue-detuned laser frequencies. We also demonstrate that the two-photon coherence leads …
Quantum coherence, the physical property underlying fundamental phenomena such as multi-particle interference and entanglement, has emerged as a valuable resource upon which exotic modern technologies are founded. In general, the most prominent adversary of quantum coherence is noise arising from the interaction of the associated dynamical system with its environment. Under certain conditions, however, the existence of noise may drive quantum and classical systems to endure intriguing nontrivial effects. Along these lines, here we demonstrate, both theoretically and experimentally, that when t…
Coherence is a familiar concept in physics: It is the driving force behind wavelike phenomena such as the diffraction of light. Moreover, wave-particle duality implies that all quantum objects can exhibit coherence, and this quantum coherence is crucial to understanding the behaviour of a plethora of systems. In this article, which is written at an undergraduate level, we shall briefly introduce what is meant by coherence in a well-known classical setting, before going on to describe its quantum version. We will show that coherence is important in describing the properties of solid-state nanos…
We derive a generalized wave-particle duality relation for arbitrary multipath quantum interference phenomena. Beyond the conventional notion of the wave nature of a quantum system, i.e., the interference fringe visibility, we introduce a quantifier as the normalized quantum coherence, recently defined in the framework of quantum information theory. To witness the particle nature, we quantify the path distinguishability or the which-path information based on unambiguous quantum state discrimination. Then, the Bohr complementarity principle for multipath quantum interference can be stated as a …
While the scaling of entanglement in a quantum system can be used to distinguish many-body quantum phases, it is usually hard to quantify the amount of entanglement in mixed states of open quantum systems, while measuring entanglement experimentally, even for the closed systems, requires in general quantum state tomography. In this work we show how to remedy this situation in system with a fixed or conserved charge, e.g., density or magnetization, due to an emerging relation between quantum correlations and coherence. First, we show how, in these cases, the presence of multipartite entanglemen…
Quantum coherence, the physical property underlying fundamental phenomena such as multi-particle interference and entanglement, has emerged as a valuable resource upon which modern technologies are founded. In general, the most prominent adversary of quantum coherence is noise arising from the interaction of the associated dynamical system with its environment. Under certain conditions, however, the existence of noise may drive quantum and classical systems to endure intriguing nontrivial effects. In this vein, here we demonstrate, both theoretically and experimentally, that when two indisting…
Quantum entanglement and coherence are two fundamental features of nature, arising from the superposition principle of quantum mechanics. While considered as puzzling phenomena in the early days of quantum theory, it is only very recently that entanglement and coherence have been recognized as resources for the emerging quantum technologies, including quantum metrology, quantum communication, and quantum computing. In this work we study the limitations for the interconversion between coherence and entanglement. We prove a fundamental no-go theorem, stating that a general resource theory of sup…
Explaining how microscopic entities collectively produce macroscopic phenomena is a fundamental goal of many-body physics. Theory predicts that large-scale entanglement is responsible for exotic macroscopic phenomena, but observation of entangled particles in naturally occurring systems is extremely challenging. Synthetic quantum systems made of atoms in optical lattices have been con- structed with the goal of observing macroscopic quantum phenomena with single-atom resolution. Serious challenges remain in producing and detecting long-range quantum correlations in these systems, however. Here…
Interaction between a quantum system and its environment can induce stationary coherences -- off-diagonal elements in the reduced system density matrix -- even at equilibrium. This work investigates the ``quantumness'' of such phenomena by examining the ability of classical and semiclassical models to describe equilibrium stationary coherence in the multi-level spin boson (MLSB) model, a common model for light-harvesting systems. A well justified classical harmonic oscillator model is found to fail to capture equilibrium coherence. This failure is attributed to the effective weakness of classi…
A field dependent $su(2)$ gauge transformation connects between the adiabatic and diabatic pictures in the (Landau-Zener-Stueckelberg) potential curve crossing problem. It is pointed out that weak and strong potential curve crossing interactions are interchanged under this transformation, and thus realizing a naive strong and weak duality. A reliable perturbation theory should thus be formulated in the both limits of weak and strong interactions. In fact, main characteristics of the potential crossing phenomena such as the Landau-Zener formula including its numerical coefficient are well-descr…
We study many-body quantum coherence and interaction blockade in two Josephson-linked Bose-Einstein condensates. We introduce universal operators for characterizing many-body coherence without limitations on the system symmetry and total particle number $N$. We reproduce the results for both coherence fluctuations and number squeezing in {\em symmetric} systems of large $N$, and reveal several peculiar phenomena that may occur in {\em asymmetric} systems and systems of small $N$. For asymmetric systems, we show that, due to an interplay between asymmetry and inter-particle interaction, the coh…
It is recognized that Grover arrived at his original quantum search algorithm inspired by his comprehension of the interference of classical waves originating from an array of antennas. It is also known that quantum-mechanical characterization of electromagnetic radiation is isomorphic to the treatment of the orientation of a spin-1/2 particle. In this paper, motivated by Grover's original intuition and starting from this mathematical equivalence, we present a quantitative link between the geometry of time-independent optimal-speed Hamiltonian evolutions on the Bloch sphere and the geometry of…
Heat exchanges are the essence of Thermodynamics. In order to investigate non-equilibrium effects like quantum coherence and correlations in heat flows we introduce the concept of apparent temperature. Its definition is based on the expression of the heat flow between out-of-equilibrium quantum systems. Such apparent temperatures contain crucial information on the role and impact of correlations and coherence in heat exchanges. In particular, both behave as populations, affecting dramatically the population balance and therefore the apparent temperatures and the heat flows. We show how seminal…
Quantum coherence quantifies the amount of superposition in a quantum system, and is the reason and resource behind several phenomena and technologies. It depends on the natural basis in which the quantum state of the system is expressed, which in turn hinges on the physical set-up being analyzed and utilized. While quantum coherence has hitherto been conceptualized by employing different categories of complete bases, there do exist interesting physical situations, where the natural basis is an incomplete one, an example being an interferometric set-up with the observer controlling only a cert…
We consider topological protection mechanisms in dissipative quantum systems in the presence of quenched disorder, with the intent to prolong coherence times of qubits. The physical setting is a network of qubits and dissipative cavities whose coupling parameters are tunable, such that topological edge states can be stabilized. The evolution of a fiducial qubit is entirely determined by a non-Hermitian Hamiltonian which thus emerges from a bona-fide physical process. It is shown how even in the presence of disorder winding numbers can be defined and evaluated in real space, as long as certain …
We theoretically investigate exciton relaxation dynamics in molecular aggregates based on model photosynthetic complexes under various conditions of incoherent excitation. We show that noise-induced quantum coherence is generated between spatially-separated exciton states which belong to the same or different energy transfer pathways, coupled via real and virtual transfer processes. Such quantum coherence effects may be used to improve light-harvesting efficiency and to reveal quantum phenomena in biology.
We present an experiment demonstrating high-resolution coherent control of a four-level atomic system in a closed (diamond) type configuration. A femtosecond frequency comb is used to establish phase coherence between a pair of two-photon transitions in cold Rb atoms. By controlling the spectral phase of the frequency comb we demonstrate the optical phase sensitive response of the diamond system. The high-resolution state selectivity of the comb is used to demonstrate the importance of the signs of dipole moment matrix elements in this type of closed-loop excitation. Finally, the pulse shape i…
Macroscopic quantum phenomena such as lasers, Bose-Einstein condensates, superfluids, and superconductors are of great importance in foundations and applications of quantum mechanics. In particular, quantum superposition of a large number of spins in solids is highly desirable for both quantum information processing and ultrasensitive magnetometry. Spin ensembles in solids, however, have rather short collective coherence time (typically less than microseconds). Here we demonstrate that under realistic conditions it is possible to maintain macroscopic quantum superposition of a large spin ensem…
We study the quantum dynamics of cold Bose atoms in a double well. It is shown that self-trapping, as well as population oscillations are common phenomena associated to nonlinear interactions. For larger $U/t$, multi-particle tunneling is damped and the quantum dynamics is dominated by the single-particle tunneling. The many-body system can be effectively described in a truncated Fock space. It exhibits coherence-decoherence oscillations in the temporal evolution. We predict a novel phenomenon of dynamical revival and collapse of matter wave fields in optical lattices in regimes near the super…
The implications of large-scale coherence in biological systems and possible links to quantum theory are only beginning to be explored. Whether quantum-like coherent phenomena are relevant, or even possible at all, at the high temperatures of biological systems remains unsettled. Here, we present a broader perspective on biological organization and how quantum-like dynamics and coherence might shape the very fabric from which complex biological systems are organized. Regardless of its exact nature, a unique form of coherence seems apparent at multiple scales in biology and its better character…
We study two models of quantum absorption refrigerators with the main focus on discerning the role of noise-induced coherence on their thermodynamic performance. Analogously to the previous studies on quantum heat engines, we find the increase in the cooling power due to the mechanism of noise-induced coherence. We formulate conditions imposed on the microscopic parameters of the models under which they can be equivalently described by classical stochastic processes and compare the performance of the two classes of fridges (effectively classical vs. truly quantum). We find that the enhanced pe…
Non-coherent evolution of closed weakly interacting system leads to equidistribution of probabilities of microstates
Departamento de Fisica de Materia Condensada, GIYA, CAC-CNEA（凝聚态物理系，GIYA，CAC-CNEA）；Instituto de Nanociencia y Nanotecnologia, INN-CONICET-CNEA（纳米科学与技术研究所，INN-CONICET-CNEA）
We study light propagation in a photonic system that shows stepwise evolution in a discretized environment. It resembles a discrete-time version of photonic waveguide arrays or quantum walks. By introducing controlled photon losses to our experimental setup, we observe unexpected effects like sub-exponential energy decay and formation of complex fractal patterns. This demonstrates that the interplay of linear losses, discreteness and energy gradients leads to genuinely new coherent phenomena in classical and quantum optical experiments. Moreover, the influence of decoherence is investigated.
Quantum mechanical phenomena, such as electronic coherence and entanglement, play a key role in achieving the unrivalled efficiencies of light-energy conversion in natural photosynthetic light-harvesting complexes, and triggered the growing interest in the possibility of organic quantum computing. Since biological systems are intrinsically heterogeneous, clear relations between structural and quantum-mechanical properties can only be obtained by investigating individual assemblies. However, single-molecule techniques to access ultrafast coherences at physiological conditions were not available…
Quantum coherence is the most distinguished signature of quantum mechanics, also recognized to be an essential resource for many promising quantum technologies, playing a central role in phenomena related to quantum information science, quantum thermodynamics and quantum biology, just to mention few examples. However, the resource theory of coherence is in the preliminary stage of its development, being still limited to the study of the manipulation and quantification of coherence, mostly from a theoretical viewpoint. Here, we propose an experimental method to directly measure the relative ent…
The entropy production in dissipative processes is the essence of the arrow of time and the second law of thermodynamics. For dissipation of quantum systems, it was recently shown that the entropy production contains indeed two contributions: a classical one and a quantum one. Here we show that for degenerate (or near-degenerate) quantum systems there are additional quantum contributions which, remarkably, can become negative. Furthermore, such negative contributions are related to significant changes in the ongoing thermodynamics. This includes phenomena such as generation of coherences betwe…
