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Quantum time dilation occurs when a clock moves in a superposition of relativistic momentum wave packets. The lifetime of an excited hydrogenlike atom can be used as a clock, which we use to demonstrate how quantum time dilation manifests in a spontaneous emission process. The resulting emission rate differs when compared with the emission rate of an atom prepared in a mixture of momentum wave packets at order v^{2}/c^{2}. This effect is accompanied by a quantum correction to the Doppler shift due to the coherence between momentum wave packets. This quantum Doppler shift affects the spectral line shape at order v/c. However, its effect on the decay rate is suppressed when compared with the effect of quantum time dilation. We argue that spectroscopic experiments offer a technologically feasible platform to explore the effects of quantum time dilation.

We report a high-accuracy measurement of the differential static scalar polarizability Δα0 of the 5s2S1/2-4d2D5/2 transition of the 88Sr+ ion. The high accuracy is obtained by comparing the micromotion-induced positive scalar Stark shift to the negative time-dilation shift. Measurement of the trap drive frequency where these shifts cancel is used to determine Δα0 without the need to determine the electric field. Δα0 is a critical parameter for the operation of frequency standards as it determines the blackbody radiation frequency shift coefficient, the largest source of uncertainty in the 88Sr+ ion clock. The measured value of Δα0 is -4.7938(71) × 10-40 J m2/V2. Taking into account the dynamic correction, the blackbody shift at 300 K is 0.247 99(37) Hz. The contribution of the blackbody shift coefficient to the uncertainty of the ion standard has been reduced by a factor of 24, from 2 × 10-17 to 8.3 ×10-19. The revised total uncertainty of our reference standard is 1.2 × 10-17, limited by the blackbody field evaluation. An additional benefit of the low uncertainty of Δα0 is the ability to suppress, by a factor of about 200, the net micromotion frequency shifts. [ABSTRACT FROM AUTHOR]

Proper time, ideal clocks, and boosts are well understood classically, but subtleties arise in quantum physics. We show that quantum clocks set in motion via momentum boosts do not witness classical time dilation. However, using velocity boosts we find the ideal behavior in both cases, where the quantum clock and classical observer are set in motion. Without internal state-dependent forces additional effects arise. As such, we derive observed frequency shifts in ion trap atomic clocks, indicating a small additional shift, and also show the emergence of nonideal behavior in a theoretical clock model.

The article presents information on a study which focuses on the high-accuracy measurement of the differential static scalar polarizability of a 88Sr(strontium)+ atomic Clock. It compares the micromotion-induced positive scalar Stark shift to the negative time-dilation shift, and measures trap drive frequency, without the need of determining the electric field.

We report on Raman sideband cooling of ^{25}Mg^{+} to sympathetically cool the secular modes of motion in a ^{25}Mg^{+}-^{27}Al^{+} two-ion pair to near the three-dimensional (3D) ground state. The evolution of the Fock-state distribution during the cooling process is studied using a rate-equation simulation, and various heating sources that limit the efficiency of 3D sideband cooling in our system are discussed. We characterize the residual energy and heating rates of all of the secular modes of motion and estimate a secular motion time-dilation shift of -(1.9±0.1)×10^{-18} for an ^{27}Al^{+} clock at a typical clock probe duration of 150 ms. This is a 50-fold reduction in the secular motion time-dilation shift uncertainty in comparison with previous ^{27}Al^{+} clocks.

We present the concluding result from an Ives-Stilwell-type time dilation experiment using 7Li+ ions confined at a velocity of β = v /c = 0.338 in the storage ring ESR at Darmstadt. A A-type three-level system within the hyperfme structure of the 7Li+3S1 → 3P2 line is driven by two laser beams aligned parallel and antiparallel relative to the ion beam. The lasers' Doppler shifted frequencies required for resonance are measured with an accuracy of < 4 × 10-9 using optical-optical double resonance spectroscopy. This allows us to verify the special relativity relation between the time dilation factor y and the velocity β, γ√ 1 - β>2 = 1 to within ±2.3 × 10-9 at this velocity. The result, which is singled out by a high boost velocity β, is also interpreted within Lorentz invariance violating test theories. [ABSTRACT FROM AUTHOR]

We present the concluding result from an Ives-Stilwell-type time dilation experiment using 7Li+ ions confined at a velocity of β=v/c=0.338 in the storage ring ESR at Darmstadt. A Λ-type three-level system within the hyperfine structure of the 7Li+3S1 →3P2 line is driven by two laser beams aligned parallel and antiparallel relative to the ion beam. The lasers' Doppler shifted frequencies required for resonance are measured with an accuracy of <4×10(-9) using optical-optical double resonance spectroscopy. This allows us to verify the special relativity relation between the time dilation factor γ and the velocity β, γ√1-β2=1 to within ±2.3×10(-9) at this velocity. The result, which is singled out by a high boost velocity β, is also interpreted within Lorentz invariance violating test theories.

We report a high-accuracy measurement of the differential static scalar polarizability Δα(0) of the 5s(2)S(1/2)-4d(2)D(5/2) transition of the (88)Sr(+) ion. The high accuracy is obtained by comparing the micromotion-induced positive scalar Stark shift to the negative time-dilation shift. Measurement of the trap drive frequency where these shifts cancel is used to determine Δα(0) without the need to determine the electric field. Δα(0) is a critical parameter for the operation of frequency standards as it determines the blackbody radiation frequency shift coefficient, the largest source of uncertainty in the (88)Sr(+) ion clock. The measured value of Δα(0) is -4.7938(71) × 10(-40) J m(2)/V(2). Taking into account the dynamic correction, the blackbody shift at 300 K is 0.247,99(37) Hz. The contribution of the blackbody shift coefficient to the uncertainty of the ion standard has been reduced by a factor of 24, from 2 × 10(-17) to 8.3 × 10(-19). The revised total uncertainty of our reference standard is 1.2 × 10(-17), limited by the blackbody field evaluation. An additional benefit of the low uncertainty of Δα(0) is the ability to suppress, by a factor of about 200, the net micromotion frequency shifts.

We predict a new class of excitations propagating along a Josephson vortex in two-dimensional Josephson junctions. These excitations are associated with the distortion of a Josephson vortex line and have an analogy with shear waves in solid mechanics. Their shapes can have an arbitrary profile, which is retained when propagating. We derive a universal analytical expression for the energy of arbitrary shape excitations, investigate their influence on the dynamics of a vortex line, and discuss conditions where such excitations can be created. Finally, we show that such excitations play the role of a clock for a relativistically moving Josephson vortex and suggest an experiment to measure a time dilation effect analogous to that in special relativity.

The fluxon dynamics in a long Josephson junction with a ferromagnetic insulating layer is investigated. It is found that the Josephson phase obeys a double sine-Gordon equation involving a bound pi fluxon solution, and the internal oscillations of the bound pair acting as a clock exhibit Lorentz reductions in their frequencies regarded as a relativistic effect in the time domain, i.e., time dilation. This is the complement to the Lorentz contraction of fluxons with no clock. A possible observation scheme is also discussed.

An improved test of time dilation in special relativity has been performed using laser spectroscopy on fast ions at the heavy-ion storage-ring TSR in Heidelberg. The Doppler-shifted frequencies of a two-level transition in 7Li+ ions at v=0.064c have been measured in the forward and backward direction to an accuracy of Deltanu/nu=1 x 10(-9) using collinear saturation spectroscopy. The result confirms the relativistic Doppler formula and sets a new limit of 2.2 x 10(-7) for deviations from the time dilation factor gamma(SR)=(1-v2/c2)(-1/2).

A correction to the article "Test of Time Dilation Using Stored Li+ Ions as Clocks at Relativistic Speed" that was published in the 2014 issue is presented.

We use the Hénon-Heiles system as a paradigmatic model for chaotic scattering to study the Lorentz factor effects on its transient chaotic dynamics. In particular, we focus on how time dilation occurs within the scattering region by measuring the time with a clock attached to the particle. We observe that the several events of time dilation that the particle undergoes exhibit sensitivity to the initial conditions. However, the structure of the singularities appearing in the escape time function remains invariant under coordinate transformations. This occurs because the singularities are closely related to the chaotic saddle. We then demonstrate using a Cantor-like set approach that the fractal dimension of the escape time function is relativistic invariant. In order to verify this result, we compute by means of the uncertainty dimension algorithm the fractal dimensions of the escape time functions as measured with an inertial frame and a frame comoving with the particle. We conclude that, from a mathematical point of view, chaotic transient phenomena are equally predictable in any reference frame and that transient chaos is coordinate invariant. [ABSTRACT FROM AUTHOR]

We report on Raman sideband cooling of 25Mg+ to sympathetically cool the secular modes of motion in a 25Mg+-27Al+ two-ion pair to near the three-dimensional (3D) ground state. The evolution of the Fock-state distribution during the cooling process is studied using a rate-equation simulation, and various heating sources that limit the efficiency of 3D sideband cooling in our system are discussed. We characterize the residual energy and heating rates of all of the secular modes of motion and estimate a secular motion time-dilation shift of -(1.9±0.1)×10-18 for an 27Al+ clock at a typical clock probe duration of 150 ms. This is a 50-fold reduction in the secular motion time-dilation shift uncertainty in comparison with previous 27Al+ clocks. [ABSTRACT FROM AUTHOR]

We report a microscopic observation of the time-dependent dynamic tube dilation process on isofrictional bidisperse melts. By applying neutron spin echo (NSE) and dielectric techniques on blends of long polyisoprene (PI) chains with short PI additives with different topology, we access the dynamics of the tube dilation process on a molecular scale. The time-dependent tube dilation is directly revealed by NSE as an additional time dependence of the dynamic structure factor in the local reptation regime. We identify the characteristic time of tube dilation as the terminal time of the additive. [ABSTRACT FROM AUTHOR]

Toy models for quantum evolution in the presence of closed timelike curves have gained attention in the recent literature due to the strange effects they predict. The circuits that give rise to these effects appear quite abstract and contrived, as they require nontrivial interactions between the future and past that lead to infinitely recursive equations. We consider the special case in which there is no interaction inside the closed timelike curve, referred to as an open timelike curve (OTC), for which the only local effect is to increase the time elapsed by a clock carried by the system. Remarkably, circuits with access to OTCs are shown to violate Heisenberg's uncertainty principle, allowing perfect state discrimination and perfect cloning of coherent states. The model is extended to wave packets and smoothly recovers standard quantum mechanics in an appropriate physical limit. The analogy with general relativistic time dilation suggests that OTCs provide a novel alternative to existing proposals for the behavior of quantum systems under gravity. [ABSTRACT FROM AUTHOR]

We propose a feasible laboratory interferometry experiment with matter waves in a gravitational potential caused by a pair of artificial field-generating masses. It will demonstrate that the presence of these masses (and, for moving atoms, time dilation) induces a phase shift, even if it does not cause any classical force. The phase shift is identical to that produced by the gravitational redshift (or time dilation) of clocks ticking at the atom's Compton frequency. In analogy to the Aharonov-Bohm effect in electromagnetism, the quantum mechanical phase is a function of the gravitational potential and not the classical forces. [ABSTRACT FROM AUTHOR]

Phase compensated optical fiber links enable high accuracy atomic clocks separated by thousands of kilometers to be compared with unprecedented statistical resolution. By searching for a daily variation of the frequency difference between four strontium optical lattice clocks in different locations throughout Europe connected by such links, we improve upon previous tests of time dilation predicted by special relativity. We obtain a constraint on the Robertson-Mansouri-Sexl parameter |α|≲1.1×10-8, quantifying a violation of time dilation, thus improving by a factor of around 2 the best known constraint obtained with Ives-Stilwell type experiments, and by 2 orders of magnitude the best constraint obtained by comparing atomic clocks. This work is the first of a new generation of tests of fundamental physics using optical clocks and fiber links. As clocks improve, and as fiber links are routinely operated, we expect that the tests initiated in this Letter will improve by orders of magnitude in the near future. [ABSTRACT FROM AUTHOR]

Applying quantum field theory on a classical, curved space-time has led to the enthralling theoretical predictions of, e.g., black hole evaporation and particle creation in the early, expanding universe. However, the prospects of observing such in the near to mid future seem far from practical. This is discouraging because extrapolation of general relativity “down to the Hilbert space level,” though expected, carries no empirical support as of yet. On the other hand, fueled by the continuing developments in quantum technology, there has been growing interest in the prospect of observing more modest effects of general relativity at the level of quantum interference phenomena. Motivated by these recent developments, in this work, we investigate the Hong-Ou-Mandel (HOM) effect—a two-photon quantum-interference effect—in the space-time of a rotating spherical mass. In particular, we propose and analyze a common-path setup restricted to the surface of the Earth and show that, in principle, gravitational frame dragging induces observable shifts in the two-photon HOM dip. For completeness and correspondence with current literature, we also analyze the emergence of gravitational time dilation, for a dual-arm interferometer. The formalism thus presented establishes a basis for encoding general-relativistic effects into local, multiphoton, quantum-interference experiments. We also consider signatures of noninertial reference-frame effects on two-photon interference such as, e.g., the Sagnac effect induced by Earth's rotation, which seems detectable with current quantum-optical technology. This can be viewed as a stepping-stone towards the more ambitious goal of observing gravitational frame dragging at the level of individual photons.

We describe an optical atomic clock based on quantum-logic spectroscopy of the ¹S0↔³P0 transition in 27Al+ with a systematic uncertainty of 9.4×10-19 and a frequency stability of 1.2×10-15/√τ. A 25Mg+ ion is simultaneously trapped with the 27Al+ ion and used for sympathetic cooling and state readout. Improvements in a new trap have led to reduced secular motion heating, compared to previous 27Al+ clocks, enabling clock operation with ion secular motion near the three-dimensional ground state. Operating the clock with a lower trap drive frequency has reduced excess micromotion compared to previous 27Al+ clocks. Both of these improvements have led to a reduced time-dilation shift uncertainty. Other systematic uncertainties including those due to blackbody radiation and the second-order Zeeman effect have also been reduced. [ABSTRACT FROM AUTHOR]

We derive an action whose equations of motion contain the Poisson equation of Newtonian gravity. The construction requires a new notion of Newton-Cartan geometry based on an underlying symmetry algebra that differs from the usual Bargmann algebra. This geometry naturally arises in a covariant 1/c expansion of general relativity, with c being the speed of light. By truncating this expansion at subleading order, we obtain the field content and transformation rules of the fields that appear in the action of Newtonian gravity. The equations of motion generalize Newtonian gravity by allowing for the effect of gravitational time dilation due to strong gravitational fields. [ABSTRACT FROM AUTHOR]

We present a relativistic model for light sails of arbitrary reflectivity and absorptance undertaking nonrectilinear motion. Analytical solutions for a constant driving power and a reduced model for straight motion with an arbitrary sail's illumination are given, including for the case of a perfectly reflecting light sail examined in earlier works. When the sail is partially absorbing incoming radiation, its rest mass and temperature increase, an effect completely discarded in previous works. It is shown how sailing at relativistic velocities is intricate due to the existence of an unstable fixed point, when the sail is parallel to the incoming radiation beam, surrounded by two attractors corresponding to two different regimes of radial escape. We apply this model to the Starshot project by showing several important points for mission design. First, any misalignment between the driving light beam and the direction of the sail's motion is naturally swept away during acceleration toward relativistic speed, yet leads to a deviation of about 80 A.U. in the case of an initial misalignment of 1 arc sec for a sail accelerated up to 0.2c toward Alpha Centauri. Then, the huge proper acceleration felt by the probes (of order 2500 g), the tremendous energy cost (of about 13 kt per probe) for poor efficiency (of about 3%), the trip duration (between 22 and 33 years), the temperature at thermodynamic equilibrium (about 1500K), and the time dilation aboard (about 160-days difference) are all presented and their variation with the sail's reflectivity is discussed. We also present an application to single trips within the Solar System using double-stage light sails. A spaceship of mass 24 tons can start from Earth and stop at Mars in about seven months with a peak velocity of 30 km/s but at the price of a huge energy cost of about 5.3×10^{4} GW h due to extremely low efficiency of the directed energy system, around 10^{−4} in this low-velocity case.

The creation of delocalized coherent superpositions of quantum systems experiencing different relativistic effects is an important milestone in future research at the interface of gravity and quantum mechanics. This milestone could be achieved by generating a superposition of quantum clocks that follow paths with different gravitational time dilation and investigating the consequences on the interference signal when they are eventually recombined. Light-pulse atom interferometry with elements employed in optical atomic clocks is a promising candidate for that purpose, but it suffers from major challenges including its insensitivity to the gravitational redshift in a uniform field. All of these difficulties can be overcome with the novel scheme presented here, which is based on initializing the clock when the spatially separate superposition has already been generated and performing a doubly differential measurement where the differential phase shift between the two internal states is compared for different initialization times. This scheme can be exploited to test the universality of the gravitational redshift with delocalized coherent superpositions of quantum clocks, and it is argued that its experimental implementation should be feasible with a new generation of 10-meter atomic fountains that will soon become available. Interestingly, the approach also offers significant advantages for more compact setups based on guided interferometry or hybrid configurations. Furthermore, in order to provide a solid foundation for the analysis of the various interferometry schemes and the effects that can be measured with them, a general formalism for a relativistic description of atom interferometry in curved spacetime is developed. It can describe freely falling atoms as well as the effects of external forces and guiding potentials, and it can be applied to a very wide range of situations. As an important ingredient for quantum-clock interferometry, suitable diffraction mechanisms for atoms in internal-state superpositions are investigated too. Finally, the relation of the proposed doubly differential measurement scheme to other experimental approaches and to tests of the universality of free fall is discussed in detail.

Light axionic dark matter, motivated by string theory, is increasingly favored for the "no weakly interacting massive particle era". Galaxy formation is suppressed below a Jeans scale of ≃108 M⊙ by setting the axion mass to mB∼10-22 eV, and the large dark cores of dwarf galaxies are explained as solitons on the de Broglie scale. This is persuasive, but detection of the inherent scalar field oscillation at the Compton frequency ωB=(2.5 months)-1(mB/10-22 eV) would be definitive. By evolving the coupled Schrödinger-Poisson equation for a Bose-Einstein condensate, we predict the dark matter is fully modulated by de Broglie interference, with a dense soliton core of size ≃150 pc, at the Galactic center. The oscillating field pressure induces general relativistic time dilation in proportion to the local dark matter density and pulsars within this dense core have detectably large timing residuals of ≃400 nsec/(mB/10-22 eV). This is encouraging as many new pulsars should be discovered near the Galactic center with planned radio surveys. More generally, over the whole Galaxy, differences in dark matter density between pairs of pulsars imprints a pairwise Galactocentric signature that can be distinguished from an isotropic gravitational wave background. [ABSTRACT FROM AUTHOR]

One-dimensional topological superconductors are known to host Majorana zero modes at domain walls terminating the topological phase. Their non-Abelian nature allows for processing quantum information by braiding operations that are insensitive to local perturbations, making Majorana zero modes a promising platform for topological quantum computation. Motivated by the ultimate goal of executing quantum-information processing on a finite time scale, we study domain walls moving at a constant velocity. We exploit an effective Lorentz invariance of the Hamiltonian to obtain an exact solution of the associated quasiparticle spectrum and wave functions for arbitrary velocities. Essential features of the solution have a natural interpretation in terms of the familiar relativistic effects of Lorentz contraction and time dilation. We find that the Majorana zero modes remain stable as long as the domain wall moves at subluminal velocities with respect to the effective speed of light of the system. However, the Majorana bound state dissolves into a continuous quasiparticle spectrum after the domain wall propagates at luminal or even superluminal velocities. This relativistic catastrophe implies that there is an upper limit for possible braiding frequencies even in a perfectly clean system with an arbitrarily large topological gap. We also exploit our exact solution to consider domain walls moving past static impurities present in the system.

We describe a framework for calculating the frequency shift and uncertainty of trapped-ion optical atomic clocks caused by background-gas collisions, and apply this framework to an 27 Al + clock to enable a total fractional systematic uncertainty below 10 -18 . For this clock, with 38(19) nPa of room-temperature H 2 background gas, we find that collisional heating generates a non-thermal distribution of motional states with a mean time-dilation shift of order 10 -16 at the end of a 150 ms probe, which is not detected by sideband thermometry energy measurements. However, the contribution of collisional heating to the spectroscopy signal is highly suppressed and we calculate the BGC shift to be -0.6(2.4) × 10 -19 , where the shift is due to collisional heating time dilation and the uncertainty is dominated by the worst case ± π /2 bound used for collisional phase shift of the 27 Al + superposition state. We experimentally validate the framework and determine the background-gas pressure in situ using measurements of the rate of collisions that cause reordering of mixed-species ion pairs.

We describe an optical atomic clock based on quantum-logic spectroscopy of the ^{1}S&#95;{0}↔^{3}P&#95;{0} transition in ^{27}Al^{+} with a systematic uncertainty of 9.4×10^{-19} and a frequency stability of 1.2×10^{-15}/sqrt[τ]. A ^{25}Mg^{+} ion is simultaneously trapped with the ^{27}Al^{+} ion and used for sympathetic cooling and state readout. Improvements in a new trap have led to reduced secular motion heating, compared to previous ^{27}Al^{+} clocks, enabling clock operation with ion secular motion near the three-dimensional ground state. Operating the clock with a lower trap drive frequency has reduced excess micromotion compared to previous ^{27}Al^{+} clocks. Both of these improvements have led to a reduced time-dilation shift uncertainty. Other systematic uncertainties including those due to blackbody radiation and the second-order Zeeman effect have also been reduced.

We outline the solution of a fundamental problem in quantum theory which has hitherto lacked a proper solution, namely, finding the requisite quantum theoretical framework guaranteeing that the calculated inverse spontaneous emission rate of a moving atom, as a composite system of charged particles interacting with the Maxwell field, is slowed down exactly as in time dilation.