Quantum Clock Research Articles

Coherence distillation machines are impossible in quantum thermodynamics

The role of coherence in quantum thermodynamics has been extensively studied in the recent years and it is now well-understood that coherence between different energy eigenstates is a resource independent of other thermodynamics resources, such as work. A fundamental remaining open question is whether the laws of quantum mechanics and thermodynamics allow the existence of a coherence distillation machine, i.e., a machine that, by possibly consuming work, obtains pure coherent states from mixed states, at a nonzero rate. This is related to another fundamental question: Starting from many copies of noisy quantum clocks which are (approximately) synchronized with a reference clock, can one distill synchronized clocks in pure states, at a non-zero rate? Surprisingly, we find that the answer to both questions is negative for generic (full-rank) mixed states. However, at the same time, it is possible to distill a sub-linear number of pure coherent states with a vanishing error.

An Atomic-Array Optical Clock with Single-Atom Readout

Currently, the most accurate and stable clocks use optical interrogation of either a single ion or an ensemble of neutral atoms confined in an optical lattice. Here, we demonstrate a new optical clock system based on an array of individually trapped neutral atoms with single-atom readout, merging many of the benefits of ion and lattice clocks as well as creating a bridge to recently developed techniques in quantum simulation and computing with neutral atoms. We evaluate single-site resolved frequency shifts and short-term stability via self-comparison. Atom-by-atom feedback control enables direct experimental estimation of laser noise contributions. Results agree well with an ab initio Monte Carlo simulation that incorporates finite temperature, projective read-out, laser noise, and feedback dynamics. Our approach, based on a tweezer array, also suppresses interaction shifts while retaining a short dead time, all in a comparatively simple experimental setup suited for transportable operation. These results establish the foundations for a third optical clock platform and provide a novel starting point for entanglement-enhanced metrology, quantum clock networks, and applications in quantum computing and communication with individual neutral atoms that require optical clock state control.

Observation of 1S0 → 3P0 Transition of a 40Ca+ - 27Al+ Quantum Logic Clock**Supported by the National Key R&D Program of China under Grant No 2017YFA0304401, the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No XDB21030100, and the Technical Innovation Program of Hubei Province under Grant No 2018AAA045.

We report the realization of quantum logic spectroscopy on the 1S0→ 3P0 clock transition of a single 27Al+ ion. This ion is trapped together with a 40Ca+ ion in a linear Paul trap, coupled by Coulomb repulsion, which provides sympathetic Doppler laser cooling and also the means for internal state detection of the clock state of the 27Al+ ion. A repetitive quantum nondemolition measurement is performed to improve the fidelity of state detection. These techniques are applied to obtain clock spectroscopy at approximately 45 Hz. We also perform the preliminary locking on the 1S0 → 3P0 clock transition. Our work is a fundamental step that is necessary toward obtaining an ultra-precision quantum logic clock based on 40Ca+-27Al+ ions.

Skew informations from an operational view via resource theory of asymmetry

The Wigner-Yanase skew information was proposed to quantify the information contained in quantum states with respect to a conserved additive quantity, and it was later extended to the Wigner-Yanase-Dyson skew informations. Recently, the Wigner-Yanase-Dyson skew informations have been recognized as valid resource measures for the resource theory of asymmetry, and their properties have been investigated from a resource-theoretic perspective. The Wigner-Yanse-Dyson skew informations have been further generalized to a class called metric-adjusted skew informations, and this general family of skew informations have also been found to be valid asymmetry monotones. Here, we analyze this general family of the skew informations from an operational point of view by utilizing the fact that they are valid asymmetry resource monotones. We show that such an approach allows for clear physical meanings as well as simple proofs of some of the basic properties of the skew informations. Notably, we constructively prove that any type of skew information cannot be superadditive, where the violation of the superadditivity had been only known for a specific class of skew informations with numerical counterexamples. We further show a weaker version of superadditivity relation applicable to the general class of the skew informations, which proves a conjecture made for the Wigner-Yanase skew information as a special case. We finally discuss an application of our results for a situation where quantum clocks are distributed to multiple parties.

Systematic Construction of Scarred Many-Body Dynamics in 1D Lattice Models.

We introduce a family of nonintegrable 1D lattice models that feature robust periodic revivals under a global quench from certain initial product states, thus generalizing the phenomenon of many-body scarring recently observed in Rydberg atom quantum simulators. Our construction is based on a systematic embedding of the single-site unitary dynamics into a kinetically constrained many-body system. We numerically demonstrate that this construction yields new families of models with robust wave-function revivals, and it includes kinetically constrained quantum clock models as a special case. We show that scarring dynamics in these models can be decomposed into a period of nearly free clock precession and an interacting bottleneck, shedding light on their anomalously slow thermalization when quenched from special initial states.

Parallel-in-time optical simulation of history states

We present an experimental optical implementation of a parallel-in-time discrete model of quantum evolution, based on the entanglement between the quantum system and a finite dimensional quantum clock. The setup is based on a programmable spatial light modulator which entangles the polarization and transverse spatial degrees of freedom of a single photon. It enables the simulation of a qubit history state containing the whole evolution of the system, capturing its main features in a simple and configurable scheme. We experimentally determine the associated system-time entanglement, which is a measure of distinguishable quantum evolution, and also the time average of observables, which in the present realization can be obtained through one single measurement.

Multipartite Quantum Clock Synchronization under The Influence of Unruh Thermal Noise

AbstractA protocol for multipartite quantum clock synchronization is performed under the influence of Unruh thermal noise. The dynamics of multipartite quantum system consisting of Unruh–DeWitt detectors when one of the detectors is accelerated are obtained. To estimate the time difference between the clocks, the time probability is calculated and how the probability is influenced by the Unruh thermal noise and other factors is analyzed. It is shown that both relativistic motion and interaction between the atom and the external scalar field affect the choice of optimal number of excited atoms in the initial state, which leads to a higher clock adjustment accuracy. Time probabilities for different types of initial states approach the same value in the limit of infinite acceleration, while tend to different minimums with increasing number of atoms. In addition, the accuracy of clock synchronization using a pair of entangled clocks in two‐party system is always higher than in a multipartite system, while the optimal Z‐type multipartite initial state always performs better than the W‐type state.

Synchronization and Estimation of Gravity‐Induced Time Difference for Quantum Clocks

AbstractIt has recently been reported that, under an operational definition of time, quantum clocks would get entangled through gravitational effects. Here, an alternative scenario is studied: The clocks have different masses and energy gaps, which would produce time differences via gravitational interaction. The proposal of quantum clock synchronization (QCS) for the gravity‐induced time difference is discussed. It is illustrated how the stability of measurement probability in the QCS proposal is influenced by the gravitational interaction induced by the clocks themselves. It is found that the precision of clock synchronization depends on the energy gaps of the clocks and the improvement of precision in quantum metrology is in fact an indicator of entanglement generation. The quantum enhanced estimation of time difference is also presented and it is found that the quantum Fisher information is very sensitive to the distance between the clocks.

Unleashing quantum into the world [quantum applications

The author discusses the application of quantum technologies in the real world, from a UK perspective. The paper concentrates on quantum communication over fibre networks and over space links. Quantum key distribution is also considered. Mention is briefly made of quantum clock technology and quantum gravity sensors.

Quantum thermal absorption machines: refrigerators, engines and clocks

The inexorable miniaturisation of technologies, the relentless drive to improve efficiency and the enticing prospect of boosting performance through quantum effects are all compelling reasons to investigate microscopic machines. Thermal absorption machines are a particularly interesting class of device that operate autonomously and use only heat flows to perform a useful task. In the quantum regime, this provides a natural setting in which to quantify the thermodynamic cost of various operations such as cooling, timekeeping or entanglement generation. This article presents a pedagogical introduction to the physics of quantum absorption machines, covering refrigerators, engines and clocks in detail.

Entropic Energy-Time Uncertainty Relation.

Energy-time uncertainty plays an important role in quantum foundations and technologies, and it was even discussed by the founders of quantum mechanics. However, standard approaches (e.g., Robertson's uncertainty relation) do not apply to energy-time uncertainty because, in general, there is no Hermitian operator associated with time. Following previous approaches, we quantify time uncertainty by how well one can read off the time from a quantum clock. We then use entropy to quantify the information-theoretic distinguishability of the various time states of the clock. Our main result is an entropic energy-time uncertainty relation for general time-independent Hamiltonians, stated for both the discrete-time and continuous-time cases. Our uncertainty relation is strong, in the sense that it allows for a quantum memory to help reduce the uncertainty, and this formulation leads us to reinterpret it as a bound on the relative entropy of asymmetry. Because of the operational relevance of entropy, we anticipate that our uncertainty relation will have information-processing applications.

History state formalism for Dirac’s theory

We propose a history state formalism for a Dirac particle. By introducing a reference quantum clock system it is first shown that Dirac's equation can be derived by enforcing a timeless Wheeler-DeWitt-like equation for a global state. The Hilbert space of the whole system constitutes a unitary representation of the Lorentz group with respect to a properly defined invariant product, and the proper normalization of global states directly ensures standard Dirac's norm. Moreover, by introducing a second quantum clock, the previous invariant product emerges naturally from a generalized continuity equation. The invariant parameter $\tau$ associated with this second clock labels history states for different particles, yielding an observable evolution in the case of an hypothetical superposition of different masses. Analytical expressions for both space-time density and electron-time entanglement are provided for two particular families of electron's states, the former including Pryce localized particles.

Simulation and realization of a second-order quantum-interference-based quantum clock synchronization at the femtosecond level.

Quantum clock synchronization schemes utilizing frequency-entangled pulses have flourished for their potentially superior precision to the classical protocols. In this Letter, a new experimental record based on the second-order quantum interference algorithm is reported, to the best of our knowledge. The synchronization accuracy between two parties separated by a 6km fiber coiling link, which is evaluated by the time offset shift relative to that with the fibers removed, has been measured to be 13±1 ps. The stability in terms of time deviation (TDEV) of 0.81ps at an averaging time of 100s has been achieved. The long-term synchronization stability is seen determined by the measurement device, and a minimum stability of 60fs has been reached at 25,600s. Furthermore, for the first time to the best of our knowledge, we quantify the performance of this quantum synchronization scheme, and very good agreements with the experimental results have been achieved. According to the quantum simulation, further improvements for both the synchronizing stability and accuracy can be expected.

Noncommutative geometry of the quantum clock

We introduce a model of noncommutative geometry that gives rise to the uncertainty relations recently derived from the discussion of a quantum clock. We investigate the dynamics of a free particle in this model from the point of view of doubly special relativity and discuss the geodesic motion in a Schwarzschild background.

Time in quantum mechanics: A fresh look at the continuity equation

The local conservation of a physical quantity whose distribution changes with time is mathematically described by the continuity equation. The corresponding time parameter, however, is defined with respect to an idealized classical clock. We consider what happens when this classical time is replaced by a non-relativistic quantum-mechanical description of the clock. From the clock-dependent Schr\"odinger equation (as analogue of the time-dependent Schr\"odinger equation) we derive a continuity equation, where, instead of a time-derivative, an operator occurs that depends on the flux (probability current) density of the clock. This clock-dependent continuity equation can be used to analyze the dynamics of a quantum system and to study degrees of freedom that may be used as internal clocks for an approximate description of the dynamics of the remaining degrees of freedom. As an illustration, we study a simple model for coupled electron-nuclear dynamics and interpret the nuclei as quantum clock for the electronic motion. We find that whenever the Born-Oppenheimer approximation is valid, the continuity equation shows that the nuclei are the only relevant clock for the electrons.

Autonomous Quantum Machines and Finite-Sized Clocks

Processes such as quantum computation, or the evolution of quantum cellular automata are typically described by a unitary operation implemented by an external observer. In particular, an interaction is generally turned on for a precise amount of time, using a classical clock. A fully quantum mechanical description of such a device would include a quantum description of the clock whose state is generally disturbed because of the back-reaction on it. Such a description is needed if we wish to consider finite sized autonomous quantum machines requiring no external control. The extent of the back-reaction has implications on how small the device can be, on the length of time the device can run, and is required if we want to understand what a fully quantum mechanical treatment of an observer would look like. Here, we consider the implementation of a unitary by a finite sized device which we call the "Quasi-Ideal clock", and show that the back-reaction on it can be made exponentially small in the device's dimension with only a linear increase in energy. As a result, an autonomous quantum machine need only be of modest size and or energy. We are also able to solve a long-standing open problem by using a finite sized quantum clock to approximate the continuous evolution of an Idealised clock. The result has implications on the equivalence of different paradigms of quantum thermodynamics, some which allow external control and some which only allow autonomous thermal machines.

Demonstration of multiparty quantum clock synchronization

Quantum clock synchronization (QCS) is a kind of method to measure the time difference among spatially separated clocks with the principle of quantum mechanics. The first QCS algorithm proposed by Chuang and Jozsa is merely based on two parties, which is further extended and generalized to multiparty situation by Krco and Paul. They present a multiparty QCS protocol based upon W-state, utilizing shared prior entanglement and broadcasting the classical information to synchronize spatially separated clocks. Shortly afterward, Ben-Av and Exman came up with an optimized multiparty QCS based on Z-state. In this work, we firstly report the demonstrations of these two multiparty QCS protocols in a four-qubit liquid-state nuclear magnetic resonance system. The experimental results show a great agreement with the theoretical predictions and also prove that Ben-AV’s multiparty QCS algorithm is more accurate than Krco’s.

A Probability Distribution for Quantum Tunneling Times

We propose a general expression for the probability distribution of real-valued tunneling times of a localized particle, as measured by the Salecker-Wigner-Peres quantum clock. This general expression is used to obtain the distribution of times for the scattering of a particle through a static rectangular barrier and for the tunneling decay of an initially bound state after the sudden deformation of the potential, the latter case being relevant to understand tunneling times in recent attosecond experiments involving strong field ionization.

Remote quantum clock synchronization without synchronized clocks

A major outstanding problem for many quantum clock synchronization protocols is the hidden assumption of a common phase reference between the parties to be synchronized. In general, the definition of the quantum states between two parties do not have consistent phase definitions, which can lead to an unknown systematic error. We show that despite prior arguments to the contrary, it is possible to remove this unknown phase via entanglement purification. This closes the loophole for entanglement based quantum clock synchronization protocols, which is a non-local approach to synchronize two clocks independent of the properties of the intervening medium. Starting with noisy Bell pairs, we show that the scheme produces a singlet state for any combination of (i) differing basis conventions for Alice and Bob; (ii) an overall time offset in the execution of the purification algorithm; and (iii) the presence of a noisy channel. Error estimates reveal that better performance than existing classical Einstein synchronization protocols should be achievable using current technology.

Quantum complementarity of clocks in the context of general relativity

Clocks play a special role at the interface of general relativity and quantum mechanics. We analyze a clock-interferometry thought experiment and go on to theoretically derive and experimentally test a complementarity relation for quantum clocks in the context of the gravitational time lag. The effect of time lag is simulated using a magnetic gradient. We study this relation in detail and discuss its application to various types of quantum clocks.