Measuring time means counting the occurrence of periodic phenomena. Over the past centuries a major effort was put to make stable and precise oscillators to be used as clock regulators. Here we consider a different class of clocks based on stochastic clicking processes. We provide a rigorous statistical framework to study the performances of such devices and apply our results to a single coherently driven two-level atom under photodetection as an extreme example of non-periodic clock. Quantum Jump MonteCarlo simulations and photon counting waiting time distribution will provide independent checks on the main results.
Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；University of the Basque Country UPV/EHU（巴斯克公立大学）；Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；Atominstitut, TU Wien（维也纳工业大学原子研究所）；Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）；Louisiana State University（路易斯安那州立大学）；Western University（韦仕敦大学）
All clocks, classical or quantum, are open non equilibrium irreversible systems subject to the constraints of thermodynamics. Using examples I show that these constraints necessarily limit the performance of clocks and that good clocks require large energy dissipation. For periodic clocks, operating on a limit cycle, this is a consequence of phase diffusion. It is also true for non periodic clocks (for example, radio carbon dating) but due to telegraph noise not to phase diffusion. In this case a key role is played by accurate measurements that decrease entropy, thereby raising the free energy…
The statistical state of any (classical or quantum) system with non-trivial time evolution can be interpreted as the pointer of a clock. The quality of such a clock is given by the statistical distinguishability of its states at different times. If a clock is used as a resource for producing another one the latter can at most have the quality of the resource. We show that this principle, formalized by a quasi-order, implies constraints on many physical processes. Similarly, the degree to which two (quantum or classical) clocks are synchronized can be formalized by a quasi-order of synchronism.…
This letter reports telecom-band sequential time-bin entangled photon-pair generation at a repetition rate of 10 GHz in periodically-poled reverse-proton-exchange lithium niobate waveguides based on mode demultiplexing. With up-conversion single-photon detectors, we observed a two-photon-interference-fringe visibility of 85.32% without subtraction of accidental noise contributions, which can find broad application in quantum information and quantum entanglement research.
We have constructed an optical clock with a fractional frequency inaccuracy of 8.6e-18, based on quantum logic spectroscopy of an Al+ ion. A simultaneously trapped Mg+ ion serves to sympathetically laser-cool the Al+ ion and detect its quantum state. The frequency of the 1S0->3P0 clock transition is compared to that of a previously constructed Al+ optical clock with a statistical measurement uncertainty of 7.0e-18. The two clocks exhibit a relative stability of 2.8e-15/ sqrt(tau), and a fractional frequency difference of -1.8e-17, consistent with the accuracy limit of the older clock.
We propose a multi party quantum clock synchronization protocol that makes optimal use of the maximal multipartite entanglement of GHZ-type states. To realize the protocol, different versions of maximally entangled eigenstates of collective energy are generated by local transformations that distinguish between different groupings of the parties. The maximal sensitivity of the entangled states to time differences between the local clocks can then be accessed if all parties share the results of their local time dependent measurements. The efficiency of the protocol is evaluated in terms of the s…
A fundamental description of time can be consistent not only with the usual monotonic behavior but also with a periodic physical clock variable, coupled to the degrees of freedom of a system evolving in time. Generically, one would in fact expect some kind of oscillating motion of a system that is dynamical and interacts with its surroundings, as required for a fundamental clock that can be noticed by any other system. Unitary evolution does not require a monotonic clock variable and can be achieved more generally by formally unwinding the periodic clock movement, keeping track not only of the…
Short coherence times present a primary obstacle in quantum computing and sensing applications. In atomic systems, clock transitions (CTs), formed from avoided crossings in an applied Zeeman field, can substantially increase coherence times. We show how CTs can dampen intrinsic and extrinsic sources of quantum noise in molecules. Conical intersections between two periodic potentials form CTs in electron paramagnetic resonance experiments of the spin-polarized singlet fission photoproduct. We report on a pair of CTs for a two-chromophore molecule in terms of the Zeeman field strength, molecular…
It is shown that a canonical time observable may be defined for any quantum system having a discrete set of energy eigenvalues, thus significantly generalising the known case of time observables for periodic quantum systems (such as the harmonic oscillator). The general case requires the introduction of almost-periodic probability operator measures (POMs), which allow the expectation value of any almost-periodic function to be calculated. An entropic uncertainty relation for energy and time is obtained which generalises the known uncertainty relation for periodic quantum systems. While non-per…
Quantum metrology with ultra-high precision usually requires atoms prepared in an ultra-stable environment with well-defined quantum states. Thus, in optical lattice clock systems deep lattice potentials are used to trap ultra-cold atoms. However, decoherence, induced by Raman scattering and higher order light shifts, can significantly be reduced if atomic clocks are realized in shallow optical lattices. On the other hand, in such lattices, tunneling among different sites can cause additional dephasing and strongly broadening of the Rabi spectrum. Here, in our experiment, we periodically drive…
Optical frequency comparison of the 40Ca+ clock transition ν_{Ca} (2S1/2-2D5/2, 729nm) against the 87Sr optical lattice clock transition ν_{Sr}(1S0-3P0, 698nm) has resulted in a frequency ratio ν_{Ca} / ν_{Sr} = 0.957 631 202 358 049 9(2 3). The rapid nature of optical comparison allowed the statistical uncertainty of frequency ratio ν_{Ca} / ν_{Sr} to reach 1x10-15 in only 1000s and yielded a value consistent with that calculated from separate absolute frequency measurements of ν_{Ca} using the International Atomic Time (TAI) link. The total uncertainty of the frequency ratio using optical co…
All clocks, in some form or another, use the evolution of nature towards higher entropy states to quantify the passage of time. Due to the statistical nature of the second law and corresponding entropy flows, fluctuations fundamentally limit the performance of any clock. This suggests a deep relation between the increase in entropy and the quality of clock ticks. Indeed, minimal models for autonomous clocks in the quantum realm revealed that a linear relation can be derived, where for a limited regime every bit of entropy linearly increases the accuracy of quantum clocks. But can such a linear…
We present a novel method for engineering an optical clock transition that is robust against external field fluctuations and is able to overcome limits resulting from field inhomogeneities. The technique is based on the application of continuous driving fields to form a pair of dressed states essentially free of all relevant shifts. Specifically, the clock transition is robust to magnetic shifts, quadrupole and other tensor shifts, and amplitude fluctuations of the driving fields. The scheme is applicable to either a single ion or an ensemble of ions, and is relevant for several types of ions,…
The quantum system under periodical modulation is the simplest path to understand the quantum non-equilibrium system, because it can be well described by the effective static Floquet Hamiltonian. Under the stroboscopic measurement, the initial phase is usually irrelevant. However, if two uncorrelated parameters are modulated, their relative phase can not be gauged out, so that the physics can be dramatically changed. Here, we simultaneously modulate the frequency of the lattice laser and the Rabi frequency in an optical lattice clock (OLC) system. Thanks to ultra-high precision and ultra-stabi…
How to understand the order of Floquet stationary states in the presence of external bath coupling and their statistical mechanics is challenging; the answers are important for preparations and control of those Floquet states. Here, we propose a scheme to classify the statistical distribution of Floquet states for time-periodic systems which couple to an external heat bath. If an effective Hamiltonian and a system-bath coupling operator, which are all time-independent, can be simultaneously obtained via a time-periodic unitary transformation, the statistical mechanics of the Floquet states is …
We study a classical reparametrization-invariant system, in which ``time'' is not a priori defined. It consists of a nonrelativistic particle moving in five dimensions, two of which are compactified to form a torus. There, assuming a suitable potential, the internal motion is ergodic or more strongly irregular. We consider quasi-local observables which measure the system's ``change'' in a coarse-grained way. Based on this, we construct a statistical timelike parameter, particularly with the help of maximum entropy method and Fisher-Rao information metric. The emergent reparametrization-invaria…
A thorium-229 optical nuclear clock with feedback loop
Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien（维也纳量子科学与技术中心，原子研究所，维也纳工业大学）；Bundesamt für Eich- und Vermessungswesen (BEV)（奥地利联邦计量与测量局）；Wolfgang Pauli Institut（沃尔夫冈·泡利研究所）；Institut für Erdmessung, Leibniz Universität Hannover（汉诺威莱布尼茨大学大地测量研究所）；Institute of Scientific Instruments of the CAS, v.v.i.（中国科学院科学仪器研究所）；Physikalisch-Technische Bundesanstalt (PTB)（德国物理技术联邦研究院）；Max-Born-Institute for Nonlinear Optics and Ultrafast Spectroscopy（马克斯·玻恩非线性光学和超快光谱学研究所）
