We analyze single particle coherence and interference in the presence of particle loss and derive an inequality that relates the preservation of coherence, the creation of superposition with the vacuum, and the degree of particle loss. We find that loss channels constructed using linear optics form a special subclass. We suggests a generalized spectroscopy where, in analogy with the absorption spectrum, we measure a "coherence loss spectrum" and a "superposition creation spectrum". The theory is illustrated with examples.
Quantum coherence is important in quantum mechanics, and its essence is from superposition principle. We study the coherence of any two pure states and that of their arbitrary superposition, and obtain the relationship between them. In the case that the two states have support on orthogonal subspaces, the relationship is simple, that is, the difference between the coherence of their superposition state and the average coherence of them is smaller than 1. In other cases, we obtain different and a little more complicated relationships. Furthermore, we also obtain the lower bound of coherence of …
We study the dissipative dynamics of deformed coherent states superposition. We find that such kind of superposition can be more robust against decoherence than the usual Schrodinger cat states.
We consider the superpositions of spin coherent states and study the coherence properties and spin squeezing in these states. The spin squeezing is examined using a new version of spectroscopic squeezing criteria. The results show that the antibuching effect can be enhanced and spin squeezing can be generated in the superpositions of two spin coherent states.
In this paper, we introduce a "coherence equality" that is satisfied by any classical communication -- i.e., conveyed by a localized carrier traveling along well defined directions. In contrast, this equality is violated when the carrier is prepared in a quantum superposition of communication directions. This is phrased in terms of the success probability of a certain communication task, which results to be always constant and equal to 1/2 in the classical case. On the other hand, we develop two simple quantum schemes that deviate systematically from the classical value, thus violating the coh…
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…
We consider the case of a pair of particles initially in a superposition state corresponding to a separated pair of wave packets. We calculate \emph{exactly} the time development of this non-Gaussian state due to interaction with an \emph{arbitrary} heat bath. We find that coherence decays continuously, as expected. We then investigate entanglement and find that at a finite time the system becomes separable (not entangled). Thus, we see that entanglement sudden death is also prevalent in continuous variable systems which should raise concern for the designers of entangled systems.
We propose the notion of quantum coherence for superpositions over states which are not necessarily mutually orthogonal. This anticipatedly leads to a resource theory of non-orthogonal coherence. We characterize free states and free operations in this theory, and connect the latter with free operations in the resource theory of quantum coherence for orthogonal bases. We show that the concept of non-orthogonal coherence naturally furnishes us with a wave-particle duality in quantum double-slit experiments where the channels beyond the slits are leaky between them. Furthermore, we demonstrate ex…
We present a new paradigm in the field of cavity QED by bringing out remarkable features associated with the avoided crossing of the dressed state levels of the Jaynes Cummings model. We demonstrate how the parametric couplings, realized by a second order nonlinearity in the cavity, can turn the crossing of dressed states into avoided crossings. We show how one can generate coherence between the avoided crossing of dressed states. Such coherences result, for example, in quantum beats in the excitation probability of the qubit. The quality of quantum beats can be considerably improved by adiaba…
We consider macroscopic, mesoscopic and "S-scopic" quantum superpositions of eigenstates of an observable, and develop some signatures for their existence. We define the extent, or size $S$ of a superposition, with respect to an observable \hat{x}, as being the range of outcomes of \hat{x} predicted by that superposition. Such superpositions are referred to as generalized $S$-scopic superpositions to distinguish them from the extreme superpositions that superpose only the two states that have a difference $S$ in their prediction for the observable. We also consider generalized $S$-scopic super…
The superposition principle lies at the heart of many non-classical properties of quantum mechanics. Motivated by this, we introduce a rigorous resource theory framework for the quantification of superposition of a finite number of linear independent states. This theory is a generalization of resource theories of coherence. We determine the general structure of operations which do not create superposition, find an elementary connection to unambiguous state discrimination, and propose several general quantitative superposition measures. We show that several main results from resource theories o…
Through the $η$-inner product, we investigate $\cal PT$-symmetric quantum mechanics from the viewpoint of superposition and coherence theory. It is argued that $\cal PT$-symmetric quantum systems are endowed with stationary superposition or superposition-free properties. A physical interpretation of $η$-inner product in $\mathbb C^2$ is given through the Stokes parameters, showing the difference between broken and unbroken $\cal PT$-symmetric quantum systems.
Coherent superpositions are one of the hallmarks of quantum mechanics and are vital for any quantum mechanical device to outperform the classically achievable. Generically, superpositions are verified in interference experiments, but despite their longstanding central role we know very little about how to extract the number of coherently superposed amplitudes from a general interference pattern. A fundamental issue is that performing a phase-sensitive measurement is as challenging as creating a coherent superposition, so that assuming a perfectly implemented measurement for verification of qua…
The coherence of a hyperfine-state superposition of a trapped $^{9}$Be$^+$ ion in the presence of off-resonant light is experimentally studied. It is shown that Rayleigh elastic scattering of photons that does not change state populations also does not affect coherence. Coherence times exceeding the average scattering time of 19 photons are observed. This result implies that, with sufficient control over its parameters, laser light can be used to manipulate hyperfine-state superpositions with very little decoherence.
Electronic decoherence processes in trans-polyacetylene oligomers are considered by explicitly computing the time dependent molecular polarization from the coupled dynamics of electronic and vibrational degrees of freedom in a mean-field mixed quantum-classical approximation. The oligomers are described by the SSH Hamiltonian and the effect of decoherence is incorporated by propagating an ensemble of quantum-classical trajectories with initial conditions obtained by sampling the Wigner distribution of the nuclear degrees of freedom. The decoherence for superpositions between the ground and exc…
I present a general scheme through which the evidence of a superposition involving distinct classical-like states of a macroscopic system can be probed. The scheme relies on a qubit being coupled to a macroscopic harmonic oscillator in such a way that it can be used to both prepare and probe a macroscopic superposition. Two potentially realizable implementations, one with a flux qubit coupled to a LC circuit, and the other with an ion-trap qubit coupled to the collective motion of several ions, are proposed.
We consider a method for efficient parametric generation of a laser pulse. A single laser field is injected to a three-level medium which has two lower states and one excited state. The lower states are prepared initially in a position-dependent coherent superposition state. It is shown that by proper choice of the position dependence of the superposition along the direction of propagation, the incoming field can be converted completely to a new field.
The resolution of separation of two elementary signals forming a partially coherent superposition, defined by quantum Fisher information and normalised with respect to detection probabilities, is always limited by the resolution of incoherent mixtures. However, when the partially coherent superpositions are prepared in a controlled way the precision can be enhanced by up to several orders of magnitude above this limit. Coherence also allows the sorting of information about various parameters into distinct channels as demonstrated by parameter of separation linked with the anti-phase superposit…
Due to conservation of energy we cannot directly turn a quantum system with a definite energy into a superposition of different energies. However, if we have access to an additional resource in terms of a system with a high degree of coherence, as for standard models of laser light, we can overcome this limitation. The question is to what extent coherence gets degraded when utilized. Here it is shown that coherence can be turned into a catalyst, meaning that we can use it repeatedly without ever diminishing its power to enable coherent operations. This finding stands in contrast to the degrada…
Photoionization with attosecond pulses populates hole states in the photoion. Superpositions of hole states represent ideal candidates for time-dependent spectroscopy, for example via pump-probe studies. The challenge consists in identifying pulses that create coherent superpositions of hole states while satisfying practical constraints. Here, we employ quantum optimal control to maximize the degree of coherence between these hole states. To this end, we introduce a derivative-free optimization method with Sequential PArametrization update (SPA-optimization). We demonstrate the versatility and…
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…
Quantum coherence is one of the clearest departures from classical physics, exhibited when a system is in a superposition of different basis states. Here the coherent superposition of three motional Fock states of a single trapped ion is experimentally certified, with a procedure provably robust against imperfect operation. As the motional state cannot be directly interrogated, our scheme uses an interference pattern generated by projective measurement of the coupled qubit state. The minimum number of coherently superposed states is inferred from a series of threshold values based on analysis …
We present a scheme for controlling the decoherence of a linear superposition of two coherent states with opposite phases in a high-Q microwave cavity, based on the injection of appropriately prepared ``probe'' and ``feedback'' Rydberg atoms, improving the one presented in [D. Vitali et al., Phys. Rev. Lett. 79, 2442 (1997)]. In the present scheme, the information transmission from the probe to the feedback atom is directly mediated by a second auxiliary cavity. The detection efficiency for the probe atom is no longer a critical parameter, and the decoherence time of the superposition state ca…
We consider the simultaneous propagation of a pair of Raman-resonant, frequency-modulated (chirped) laser pulses in an optically thick medium, modeled by an ensemble of $Λ$-atoms. A self-organization ('matching`) effect is shown for the chirped pulse pair, which leads to a quasi-lossless propagation. Furthermore, we demonstrate that a well-defined coherent superposition of the atomic ground states and, correspondingly, a coherence is robustly created in the medium that can be controlled by amplitudes of the laser pulses. The proposed scheme can be applied to substantially increase the efficien…
Motivated by our observation of fast echo decay and a surprising coherence freeze, we have developed a pump-probe spectroscopy technique for vibrational states of ultracold $^{85}$Rb atoms in an optical lattice to gain information about the memory dynamics of the system. We use pump-probe spectroscopy to monitor the time-dependent changes of frequencies experienced by atoms and to characterize the probability distribution of these frequency trajectories. We show that the inferred distribution, unlike a naive microscopic model of the lattice, correctly predicts the main features of the observed…
Coherence arises from the superposition principle and plays a key role in quantum mechanics. Recently, Baumgratz et al. [T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett. 113, 140401 (2014)] established a rigorous framework for quantifying the coherence of finite dimensional quantum states. In this work we provide a framework for quantifying the coherence of Gaussian states and explicitly give a coherence measure based on the relative entropy.
We show that the quantum states generated by universal optimal quantum cloning of a single photon represent an universal set of quantum superpositions resilient to decoherence. We adopt Bures distance as a tool to investigate the persistence ofquantum coherence of these quantum states. According to this analysis, the process of universal cloning realizes a class of quantum superpositions that exhibits a covariance property in lossy configuration over the complete set of polarization states in the Bloch sphere.
We investigate the role of quantum coherence in the efficiency of excitation transfer in a ring-hub arrangement of interacting two-level systems, mimicking a light-harvesting antenna connected to a reaction center as it is found in natural photosynthetic systems. By using a quantum jump approach, we demonstrate that in the presence of quantum coherent energy transfer and energetic disorder, the efficiency of excitation transfer from the antenna to the reaction center depends intimately on the quantum superposition properties of the initial state. In particular, we find that efficiency is sensi…
We develop criteria sufficient to enable detection of macroscopic coherence where there are not just two macroscopically distinct outcomes for a pointer measurement, but rather a spread of outcomes over a macroscopic range. The criteria provide a means to distinguish a macroscopic quantum description from a microscopic one based on mixtures of microscopic superpositions of pointer-measurement eigenstates. The criteria are applied to Gaussian-squeezed and spin-entangled states.
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…
Charge-based qubits have been proposed as fundamental elements for quantum computers. One commonly proposed readout device is the single-electron transistor (SET). SETs can distinguish between localized charge states, but lack the sensitivity to directly distinguish superposition states, which have greatly enhanced coherence times compared with position states. We propose introducing a third dot, and exploiting energy dependent tunnelling from the qubit into this dot (bias spectroscopy) for pseudo-spin to charge conversion and superposition basis readout. We introduce an adiabatic fast passage…
Entanglement can modify the interference patterns of multi-particle systems. We analyse, using the path integral formalism, a novel example of multi-particle interference and some unexplored aspects of this phenomenon by considering the two-slit arrangement with two distinguishable particles in a superposition state. The two components of entanglement, multiplicity of multi-particle terms and their coherence, can be studied separately by comparing the patterns of product, mixed and superposition states. This suggests a scheme to detect multi-particle superposition in some favourable cases. Mor…
Quantum information science is driving progress in a vast number of scientific and technological areas that cover molecular spectroscopy and matter-light interactions in general. In these fields, the ability to generate quantum mechanically-entangled photons is opening avenues to explore the interaction of molecules with quantum light. This work considers an alternative way of correlating photons by including energy superpositions. We study how the multichromatic quantum superposition, or color superposition of photon-pair states, influences the optical properties of organic chromophores. This…
Quantum Schrodinger cat states are of great interest in quantum communications and quantum optics. These states are used in various scientific fields such as quantum computing, quantum error correction and high-precision measurements. The analysis of the Schrodinger cat states coherence is an important task for their complete practical application. Our developed approach makes it possible to estimate the coherence of the quantum Schrodinger cat state of arbitrary dimension, as well as to find the interference visibility of the state - an important optical characteristic. The obtained simple qu…
The high resilience to de-coherence shown by a recently discovered Macroscopic Quantum Superposition (MQS) involving a number of photons in excess of 5 x 10^4 motivates the present theoretical and numerical investigation. The results are placed in close comparison with the properties of the well known MQS based on |alpha> states. The very critical decoherence properties of the latter MQS are found to be fully accounted for, in a direct a simple way, by a unique "universal" function: indeed a new property of the quantum "coherent states".
One central study that constitutes a major branch of quantum resource theory is the hierarchy of states. This provides a broad understanding of resourcefulness in certain tasks in terms of efficiency. Here, we investigate the maximal superposition states, i.e., golden states, of the resource theory of superposition. Golden states in the resource theory of coherence are very well established; however, it is a very challenging task for superposition due to the nonorthogonality of the basis states. We show that there are sets of inner product settings that admit a golden state in high-dimensional…
In the presence of conservation laws, superpositions of eigenstates of the corresponding conserved quantities cannot be generated by quantum dynamics. Thus, any such coherence represents a potentially valuable resource of asymmetry, which can be used, for example, to enhance the precision of quantum metrology or to enable state transitions in quantum thermodynamics. Here we ask if such superpositions, already present in a reference system, can be broadcast to other systems, thereby distributing asymmetry indefinitely at the expense of creating correlations. We prove a no-go theorem showing tha…
We investigate decoherence of quantum superpositions induced by gravitational time dilation and spontaneous emission between two atomic levels. It has been shown that gravitational time dilation can be an universal decoherence source. Here, we consider decoherence induced by gravitational time dilation only in the situation of spontaneous emission. Then, we obtain that the coherence of particle's position state depends on reference frame due to the time dilation changing the distinguishability of emission photon from two positions of particle. Changing the direction of light field can also res…
The high resilience to de-coherence shown by a recently discovered Macroscopic Quantum Superposition (MQS) generated by a quantum injected optical parametric amplifier (QI-OPA) and involving a number of photons in excess of 5x10^4 motivates the present theoretical and numerical investigation. The results are analyzed in comparison with the properties of the MQS based on coherent states and NOON states, in the perspective of the comprehensive theory of the subject by W.H.Zurek. In that perspective the concepts of "pointer state", "einselection" are applied to the new scheme.
Molecular ro-vibronic coherences, joint energy-time distributions of quantum amplitudes, are selectively prepared, manipulated, and imaged in Time-Frequency-Resolved Coherent Anti-Stokes Raman Scattering (TFRCARS) measurements using femtosecond laser pulses. The studies are implemented in iodine vapor, with its thermally occupied statistical ro-vibrational density serving as initial state. The evolution of the massive ro-vibronic superpositions, consisting of 1000 eigenstates, is followed through two-dimensional images. The first- and second-order coherences are captured using time-integrated …
We present experimental results which demonstrate that nuclear magnetic resonance spectroscopy is capable of efficiently emulating many of the capabilities of quantum computers, including unitary evolution and coherent superpositions, but without attendant wave-function collapse. Specifically, we have: (1) Implemented the quantum XOR gate in two different ways, one using Pound-Overhauser double resonance, and the other using a spin-coherence double resonance pulse sequence; (2) Demonstrated that the square root of the Pound-Overhauser XOR corresponds to a conditional rotation, thus obtaining a…
Quantum spectroscopy with single two level systems has considerably improved our ability to detect weak signals. Recently it was realized that for classical signals, precision and resolution of quantum spectroscopy is limited mainly by coherence of the signal and stability of the clock used to measure time. The coherence time of the quantum probe, which can be significantly shorter, is not a major limiting factor in resolution measurements. Here, we address a similar question for spectroscopy of quantum signals, for example a quantum sensor is used to detect a single nuclear spin. We present a…
We present a study of the coherence properties of a variety of motional states of a single ion confined in a Penning ion trap. We demonstrate that the motion of the ion has a coherence time of the order of one second, using Ramsey interferometry. We introduce a technique for preparing the ion in an incoherent superposition of highly-excited motional states using a simple modification of optical sideband cooling. Coherent manipulation of these states allow measurements of optical and motional coherence to be carried out. We show that these highly-excited motional state superpositions have long …
We showed that quantum mechanical superposition can sustain in the process of ion transfer in protein membrane for a substantial period, in spite of the presence of the interactions with environmental modes of molecular vibration. The spectral temperature, as defined in quantum thermodynamical framework plays a significant role in maintaining the coherence. The ratio of decoherence time and dwell time has been calculated, which can be directly related to the degree of coherence. The results shead new light to build quantum information system of entangled ionic states in the voltage gated biolo…
One of the fundamental features of quantum mechanics is the superposition principle, a manifestation of which is embodied in quantum coherence. Coherence of a quantum state is invariably defined with respect to a preferred set of pointer states, and there exist quantum coherence measures with respect to deterministically as well as probabilistically distinguishable sets of quantum state vectors. Here we study the resource theory of quantum coherence with respect to an arbitrary set of quantum state vectors, that may not even be probabilistically distinguishable. Geometrically, a probabilistica…
The resource theory of coherence studies the operational value of superpositions in quantum technologies. A key question in this theory concerns the efficiency of manipulation and interconversion of this resource. Here we solve this question completely for mixed states of qubits by determining the optimal probabilities for mixed state conversions via stochastic incoherent operations. This implies new lower bounds on the asymptotic state conversion rate between mixed single-qubit states which in some cases is proven to be tight. Furthermore, we obtain the minimal distillable coherence for given…
We investigate the physical meaning of quantum superposition states between reactants and products in electron transfer reactions. We show that such superpositions are strongly suppressed and to leading orders of perturbation theory do not pertain in electron transfer reactions. This is because of the intermediate manifold of states separating the reactants from the products. We provide an intuitive description of these considerations with Feynman diagrams. We also discuss the relation of such quantum coherences to understanding the fundamental quantum dynamics of spin-selective radical-ion-pa…
We propose a method called `coherence swapping' which enables us to create superposition of a particle in two distinct paths, which is fed with initially incoherent, independent radiations. This phenomenon is also present for the charged particles, and can be used to swap the effect of flux line due to Aharonov-Bohm effect. We propose an optical version of the experimental set-up to test the coherence swapping. The phenomenon, which is simpler than entanglement swapping or teleportation, raises some fundamental questions about true nature of wave-particle duality, and also opens up the possibi…
We compare quantum decoherence in generic regular and chaotic systems that interact with a thermal reservoir via a dipole coupling. Using a time-dependent, self-consistent approximation in the spirit of Hartree, we derive in the high temperature limit an expression for the off-diagonal elements of the system density operator that initially corresponds to a coherent superposition of two adjacent wave packets. We relate the decoherence rate to the Lyapunov exponent in the Ehrenfest regime. In this regime, the greater the instability of the system the faster the loss of coherence occurs.
