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Here we present a liquid nitrogen-cooled Ca^+ optical clock with an overall systematic uncertainty of 3*10^-18. In contrast with the room-temperature Ca^+ optical clock that we have reported previously, the temperature of the blackbody radiation (BBR) shield in vacuum has been reduced to 82(5) K using liquid nitrogen. An ion trap with a lower heating rate and improved cooling lasers were also introduced. This allows cooling the ion temperature to the Doppler cooling limit during the clock operation, and the systematic uncertainty due to the ion's secular (thermal) motion is reduced to < 1*10^-18. The uncertainty due to the probe laser light shift and the servo error are also reduced to < 1*10^-19 and 4*10^-19 with the hyper-Ramsey method and the higher-order servo algorithm, respectively. By comparing the output frequency of the cryogenic clock to that of a room-temperature clock, the differential BBR shift between the two was measured with a fractional statistical uncertainty of 7*10^-18. The differential BBR shift was used to calculate the static differential polarizability, and it was found in excellent agreement with our previous measurement with a different method. This work suggests that the BBR shift of optical clocks can be well suppressed in a liquid nitrogen environment. This is advantageous because conventional liquid-helium cryogenic systems for optical clocks are more expensive and complicated. Moreover, the proposed system can be used to suppress the BBR shift significantly in other types of optical clocks such as Yb^+, Sr^+, Yb, Sr, etc., 15 pages, 5 figures

Optical clocks are important for precise measurements in the field of physics. As reported, both the instability and uncertainty of optical lattice clocks are more than two orders of magnitude smaller than those of the best microwave clocks. Therefore, in the near future, optical clocks could be used to redefine the second. Nevertheless, an optical clock with reliability comparable to microwave clocks has not been achieved thus far. In this paper, we compared the frequencies of two Ca^+ optical clocks that were nearly continuously operated for 31 days. Through the comparison experiment, the frequency stability of a single clocks was found to be 6.3×10^-18 at an averaging time of 520 000 s and 7.9×10^-18 at averaging time of 262000 s, while the operating uptime rate reached more than 90% in the period of around 5 days. Thus, our experiment demonstrated that it is possible to increase the stability of single-ion optical clocks to the 10^-18 level, while still maintaining quasi-continuous operation with a high operating rate. This result further confirms that optical clocks can potentially be used to redefine the second.

Highly charged ions (HCIs) are promising candidates for the next generation of atomic clocks, owing to their tightly bound electron cloud, which significantly suppresses the common environmental disturbances to the quantum oscillator. Here we propose and pursue an experimental strategy that, while focusing on various HCIs of a single atomic element, keeps the number of candidate clock transitions as large as possible. Following this strategy, we identify four adjacent charge states of nickel HCIs that offer as many as six optical transitions. Experimentally, we demonstrated the essential capability of producing these ions in the low-energy compact Shanghai-Wuhan Electron Beam Ion Trap. We measured the wavelengths of four magnetic-dipole ($M$1) and one electric-quadrupole ($E$2) clock transitions with an accuracy of several ppm with a novel calibration method; two of these lines were observed and characterized for the first time in controlled laboratory settings. Compared to the earlier determinations, our measurements improved wavelength accuracy by an order of magnitude. Such measurements are crucial for constraining the range of laser wavelengths for finding the "needle in a haystack" narrow lines. In addition, we calculated frequencies and quality factors, evaluated sensitivity of these six transitions to the hypothetical variation of the electromagnetic fine structure constant $\alpha$ needed for fundamental physics applications. We argue that all the six transitions in nickel HCIs offer intrinsic immunity to all common perturbations of quantum oscillators, and one of them has the projected fractional frequency uncertainty down to the remarkable level of 10$^{-19}$., Comment: To be published in Physical Review A

We present a robust, transportable ${\mathrm{Ca}}^{+}$ optical clock, with a systematic uncertainty of $1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$ limited by the black-body radiation (BBR) field evaluation and an uptime rate of $g75%$ over a 20-day period. The clock is then installed in an air-conditioned car trailer, making it more convenient for applications. Referenced to a stationary laboratory clock, geopotential measurements are made with the transportable clock with a total uncertainty of 0.33 m (statistically 0.25 m and systematically 0.22 m) and agree with the spirit level measurement. After being moved $g1200$ km, the absolute frequency of the ${\mathrm{Ca}}^{+}$ optical clock transition is measured as 411 042 129 776 400.41(23) Hz, with a fractional uncertainty of $5.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$, which is about one order of magnitude smaller than our previous measurement. The transportable built can be used for sub-meter-level elevation measurements, comparing intercontinental optical clocks, verifying basic physical theories, etc.

The hyperfine structures of the $2{^{3}S}_{1}$ states of the $^{6}{\mathrm{Li}}^{+}$ and $^{7}{\mathrm{Li}}^{+}$ ions are investigated theoretically to extract the Zemach radii of the $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$ nuclei by comparing with precision measurements. The obtained Zemach radii are larger than the previous values of Puchalski and Pachucki [Phys. Rev. Lett. 111, 243001 (2013)] and disagree with them by about 1.5 and 2.2 standard deviations for $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$, respectively. Furthermore, our Zemach radius of $^{6}\mathrm{Li}$ differs significantly from the nuclear physics value, derived from the nuclear charge and magnetic radii [Phys. Rev. A 78, 012513 (2008)] by more than $6\ensuremath{\sigma}$, indicating an anomalous nuclear structure for $^{6}\mathrm{Li}$. The conclusion that the Zemach radius of $^{7}\mathrm{Li}$ is about 40% larger than that of $^{6}\mathrm{Li}$ is confirmed. The obtained Zemach radii are used to calculate the hyperfine splittings of the $2{^{3}P}_{J}$ states of $\text{ }{^{6,7}\mathrm{Li}}^{+}$, where an order of magnitude improvement over the previous theory has been achieved for $^{7}{\mathrm{Li}}^{+}$.

Precision spectroscopy of ${\mathrm{Li}}^{+}$ is a promising testing ground for bound-state quantum electrodynamics (QED) and for measurements of nuclear properties such as the Zemach radius. We investigate the hyperfine and fine-structure splittings of the $2\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$ and $2{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{J}$ states of $^{7}\mathrm{Li}^{+}$ using saturated fluorescence spectroscopy based on a $\ensuremath{\sim}460\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ metastable ion beam. We measure in particular the $2\phantom{\rule{0.16em}{0ex}}^{3}S_{1}--2\phantom{\rule{0.16em}{0ex}}^{3}P_{J}$ transitions in $^{7}\mathrm{Li}^{+}$. With a triple nested loop scanning method, the long-term drift and systematic uncertainties are reduced or eliminated, resulting in a total uncertainty of less than 100 kHz. Our results are in good agreement with QED calculations. For the hyperfine splittings of $2\phantom{\rule{0.16em}{0ex}}^{3}S_{1}$, our measured values have a similar accuracy to previous measurements and theoretical calculations. For the $2{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{J}$ fine and hyperfine splittings, our measured results are one order of magnitude more accurate than those of previous measurements and have a similar accuracy to the theoretical values. The measurements lay the foundation for future work on the ${\mathrm{Li}}^{+}$ isotopes and their theoretical interpretation in terms of nuclear charge radii and the Zemach radii.

Edge states emerge in diverse areas of science, offering promising opportunities for the development of future electronic or optoelectronic devices, sound and light propagation control in acoustics and photonics. Previous experiments on edge states in photonics were carried out mostly in linear regimes, but the current belief is that nonlinearity introduces more striking features into physics of edge states, leading to the formation of edge solitons, optical isolation, making possible stable lasing in such states, to name a few. Here we report the observation of edge solitons at the zigzag edge of a reconfigurable photonic graphene lattice created via the effect of electromagnetically induced transparency in an atomic vapor cell with controllable nonlinearity. To obtain edge solitons, Raman gain is introduced to compensate strong absorption experienced by the edge state during propagation. Our observations may open the way for future experimental exploration of topological photonics on this nonlinear, reconfigurable platform., Edge states are excitations existing at the boundary of truncated periodic materials with specific spectral degeneracies, and their properties are enriched when materials possess a nonlinear response. Here, the authors provide experimental evidence of edge soliton formation in a nonlinear photonic graphene lattice induced in an atomic vapour cell.

In this work, we carry out experimental measurements and theoretical calculations of the branching fractions for the $4{P}_{3/2}$ state of $^{40}\mathrm{Ca}^{+}$. The measurements are based on counting photon numbers emitted from hundreds of ions trapped in a linear Paul trap, as their being affected by lasers. The calculations are performed using the relativistic coupled-cluster method at different approximations. The measured values for the decays of the $4{P}_{3/2}$ state into the $4{S}_{1/2}$, $3{D}_{5/2}$, and $3{D}_{3/2}$ states are, respectively, 0.9350(4), 0.0587(4), and 0.0063(2), which agree well with our recommended theoretical values 0.9344(13), 0.0590(12), and 0.0066(1). Our measured values are also consistent with the experimental values of Gerritsma et al. [R. Gerritsma, G. Kirchmair, F. Z\"ahringer, J. Benhelm, R. Blatt, and C. F. Roos, Eur. Phys. J. D 50, 13 (2008)] using a completely different method. Furthermore, we also calculate the branching fractions of the $4{P}_{1/2}$ state using the same method, and compare to the available experimental and theoretical data.

In this review, the improvements made in the past two decades for 40Ca+ optical clocks in China are presented. Uncertainty of below 1.3×10−17 was achieved by applying the “magic” RF trapping frequency and introducing a generalized Ramsey excitation scheme. The stability of 40Ca+ optical clocks has been improved to 2.5×10−15/τ with an uptime rate of 93.8% by implementing two ameliorated lock algorithms in the Ramsey excitation scheme. A long-term clock frequency comparison shows a clock stability of 6.3 × 10−18 in an averaging time of 524 000 s. A robust and transportable clock installed in an air-conditioned car trailer can achieve almost the same performance of laboratory clocks. A height difference between transportable and laboratory clocks was measured with an uncertainty of 0.33 m and the absolute frequency of 40Ca+ optical clock transitions was remeasured as 411 042 129 776 400.41(23) Hz, with a fractional uncertainty of 5.6×10−16 based on a Cs fountain clock in the National Institute of Metrology after the transportable clock was transported from Wuhan to Beijing. The author predicts that transportable single-ion optical clocks especially based on the 40Ca+ will make a significant contribution to the construction of a world-wide optical clock network and the redefinition of the unit of time in the future.

Micromotion induced by the radio-frequency field contributes greatly to the systematic frequency shifts of optical frequency standards. Although different strategies for mitigating this effect have been proposed, trapping ions optically has the potential to provide a generic solution to the elimination of micromotion. This could be achieved by trapping a single ion in the dipole trap composed of a highpower laser field. Here, we present the setup of the dipole trap composed of a 532 nm laser at a power of 10 W aiming to optically trap a single 40Ca+ and we observe an AC-Stark shift of the fluorescence spectrum line of ∼22 MHz caused by the 532 nm dipole beam. The beam waist of the dipole laser is several microns, which would provide a dipole potential strong enough for all-optical trapping of a single 40Ca+ ion.

The fractional uncertainty of the 40Ca+ optical clock in our laboratory has been evaluated to be 2.2 × 10 − 17, but it is difficult to evaluate the statistical uncertainty of the output frequency at this level, limited by the frequency stability associated with the quantum projection noise (QPN). A reduction in the stability is required to shorten the averaging time for a certain statistical uncertainty level. To improve the stability, the Ramsey method is introduced in the locking process. To improve the reliability and continuity, we introduce the idea of using auxiliary Rabi probes to avoid fringe slips in the Ramsey interrogation and to automatically search for resonance. The stability of a single 40Ca+ ion frequency standard is improved from 6.3 × 10 − 15 / τ to 2.5 × 10 − 15 / τ, where τ is the averaging time in seconds, which is close to the QPN limit for an 80-ms-long Ramsey interrogation. We obtain a stability of 1.5 × 10 − 17 at an averaging time of 21 000 s and an uptime rate of 93.8% for a 34-h-long run. These methods can easily be applied to other ion or neutral atom optical clocks.

Sympathetic cooling is a method used to lower the kinetic energy of ions with complicated energy-level structures, via Coulomb interactions with laser-cooled ions in an ion trap. The ion to be sympathetically cooled is sometimes prepared outside of the trap, and it is critical to introduce this ion into the trap by temporarily lowering the potential of one endcap without allowing the coolant ion to escape. We study the time required for a laser-cooled ion to escape from a linear Paul trap when the voltage of one endcap is lowered. The escape time is on the order of a few microseconds, and varies significantly when the low-level voltage changes. A re-cooling time of a maximum of 13 s was measured, which can be reduced to approximately one hundred of milliseconds by decreasing the duration of the low-level voltage. The measurement of these critical values lays the foundation for the smooth injection and cooling of the ion to be sympathetically cooled.

Progress of the 40Ca+ ion optical clock based on the 42S1/2 – 3d 2D5/2 electric quadrupole transition is reported. By setting the drive frequency to the “magic” frequency Ω 0, the frequency uncertainty caused by the scalar Stark shift and second-order Doppler shift induced by micromotion is reduced to the 10−19 level. By precisely measuring the differential static scalar polarizability Δα 0, the uncertainty due to the blackbody radiation (BBR) shift (coefficient) is reduced to the 10−19 level. With the help of a second-order integrating servo algorithm, the uncertainty due to the servo error is reduced to the 10−18 level. The total fractional uncertainty of the 40Ca+ ion optical clock is then improved to 2.2× 10−17, whereas this value is mainly restricted by the uncertainty of the BBR shift due to temperature fluctuations. The state preparation is introduced together with improvements in the pulse sequence, and furthermore, a better signal to noise ratio (SNR) and less dead time are achieved. The clock stability of a single clock is improved to 4.8 × 10 − 15 / τ ( in seconds ) .

We recently reported a 5×10−17 level frequency comparison of two 40Ca+ optical clocks, one of which has fractional frequency uncertainty of 3.4×10−17, limited by the BBR effect. Here we present progress towards a 40Ca+ optical clock with uncertainty at the 10−18 level. The differential static scalar polarizability Δα0 of the 40Ca+ ion clock transition is obtained by precisely measuring the “magic” rf drive frequency. Δα0 is measured as −7.2653(44)x10−40 J m2/V2, the blackbody radiation shift is then calculated to be 0.3790(2) Hz at 300 K. The contribution of the blackbody shift coefficient to the uncertainty of the optical clock at room temperature is reduced to 5.6×10−19, the excess micromotion induced clock uncertainty is also reduced to the 10−19 level by choosing the appropriate trap drive frequency. With a suppression of the BBR field temperature uncertainty to the sub-Kelvin level and improved clock stability, a robust, relatively low-cost 40Ca+ ion clock with uncertainty at 10−18 level can be made.

This paper provides a detailed description of the 40Ca+ optical frequency standard uncertainty evaluation and the absolute frequency measurement of the clock transition, as a summary and supplement for the published papers of Yao Huang et al. (Phys Rev A 84:053841, 1) and Huang et al. (Phys Rev A 85:030503, 2). The calculation of systematic frequency shifts, expected for a single trapped Ca+ ion optical frequency standard with a “clock” transition at 729 nm is described. There are several possible causes of systematic frequency shifts that need to be considered. In general, the frequency was measured with an uncertainty of 10−15 level, and the overall systematic shift uncertainty was reduced to below a part in 10−15. Several frequency shifts were calculated for the Ca+ ion optical frequency standard, including the trap design, optical and electromagnetic fields geometry and laboratory conditions, including the temperature condition and the altitude of the Ca+ ion. And we measured the absolute frequency of the 729-nm clock transition at the 10−15 level. An fs comb is referenced to a hydrogen maser, which is calibrated to the SI-second through the Global Positioning System (GPS). Using the GPS satellites as a link, we can calculate the frequency difference of the two hydrogen masers with a long distance, one in WIPM (Wuhan) and the other in National Institute of Metrology (NIM, Beijing). The frequency difference of the hydrogen maser in NIM (Beijing) and the SI-second calculated by BIPM is published on the BIPM web site every 1 month, with a time interval of every 5 days. By analyzing the experimental data obtained within 32 days of a total averaging time of >2 × 106 s, the absolute frequency of the 40Ca+ 4 s 2 S 1/2–3d 2D5/2 clock transition is measured as 411 042 129 776 393.0 (1.6) Hz with a fractional uncertainty of 3.9 × 10−15.

Linewidth narrowing and other quantum coherent effects based on three-photon coherent population trapping (CPT) in Ca+ ions are investigated. If the propagation directions of the three lasers obey the phase matching condition, the dark linewidth resulting from the CPT can be very narrow, and it can be controlled by adjusting the parameters of the lasers.

We propose a method to accelerate the revival of ion Rabi oscillation in a trapped ion system. Suitable manipulation of the frequency of the driven laser field permits us to switch from Jaynes–Cummings to off-resonant interaction. The combination of Jaynes–Cummings model and the off-resonant model induces some interesting characteristics of the ion-trap system, particularly the accelerated revival of the population of trapped ions. The amplitude of this revival is sensitive to the change of the laser frequency.

We demonstrate experimentally the existence of magic wavelengths and determine the ratio of oscillator strengths for a single trapped ion. For the first time, two magic wavelengths near 396 nm for the Ca-40(+) clock transition are measured simultaneously with high precision. By tuning the applied laser to an intermediate wavelength between transitions 4s(1/2) -> 4p(1/2) and 4s(1/2) -> 4p(3/2), the sensitivity of the clock transition Stark shift to the oscillator strengths is greatly enhanced. Furthermore, with the measured magic wavelengths, we determine the ratio of the oscillator strengths with a deviation of less than 0.5%. Our experimental method may be applied to measure magic wavelengths for other ion clock transitions. Promisingly, the measurement of these magic wavelengths paves the way to building all-optical trapped ion clocks.

In light of the diverse range of reported values for the lifetimes of metastable states of Ca-40(+), we have carried out afresh both measurements and theoretical investigation to confirm the lifetime of its 3d D-2(5/2) state (tau(3d5/2)). A high-efficiency quantum state detection method by monitoring the quantum jumps of a laser-cooled single Ca+ ion in a miniature ring Paul trap was employed in the measurement. Also, sophisticated calculations were performed considering higher order nonlinear terms in the relativistic coupled-cluster (RCC) method with all possible single and double excitations, but accounting only for the important triple excitations from both the core and the valence orbitals. Systematic factors affecting measurement, such as collision with background gases, heating effects, the power of the 866-nm laser, and state detection errors were carefully analyzed. Our observational and theoretical values for tau(3d5/2) are 1174(10) ms and 1172(3) ms, respectively, which agree well with the experimental results reported by P. A. Barton et al. [Phys. Rev. A 62, 032503 (2000)] and A. Kreuter et al. [Phys. Rev. A 71, 032504 (2005)]. The present theoretical analysis demonstrates that the contributions from the core triples and Breit interaction are notable, as they improve the theoretical results obtained in the previous RCC calculations [B. K. Sahoo, Phys. Rev. A 74, 062504 (2006)].

We propose an analytical treatment method of generation of multipartite W-type states with a single-resonant interaction of the atoms with the cavity mode in cavity QED, under the consideration of very weak decay from the excited atomic level and from the cavity mode. By manipulating different coupling strengths between the atoms and the cavity mode, we show how to deterministically produce W states, including the standard W state and the one with arbitrary coefficients. The corresponding analytical expressions are given, indicating that the detrimental influence from the atomic spontaneous emission is three times that from the cavity decay. The experimental feasibility of our scheme is also discussed by using current cavity QED techniques.

A potential scheme is proposed to generate complete sets of entangled photons in the context of cavity quantum electrodynamics (QED). The scheme includes twice interactions of atoms with cavities, in which the first interaction is made in two-mode optical cavities and the second one exists in a microwave cavity. In the optical cavities the atoms are resonant with the cavity modes, while the detuned interaction of the atoms with a single-mode of the microwave cavity is driven by a classical field. We show that our scheme is carried out with higher efficiency than previeous schemes, and is close to the reach of current technique., Comment: 7 pages, 3 figures, to appear in J. Phys. B

We introduce the general definition of the unconventional geometric phase independent of the specific physical system and show how a highly squeezed operator can approximately induce the general unconventional geometric phase, which goes beyond the original unconventional one by displacement operators (Zhu and Wang 2003 Phys. Rev. Lett. 91 187902). By means of the squeezed operator concerning the cavity mode state along a closed path in the phase space, we discuss specifically how to implement approximately a two-qubit geometric phase gate in a cavity QED system with two-photon interaction between the atoms and the cavity mode, assisted by a classical field. Discussions regarding the implementation time of the gating, the possible decaying sources and the experimental feasibility are given in detail.

We proposed a scheme to generate a multi-component squeezed coherent states with arbitrary coefficients on a line in phase space for multiple trapped ions radiated by a single standing-wave laser whose carrier frequency is tuned to the ions transition. In the scheme each ion does not need to be exactly positioned at the node of the standing wave. Furthermore, our scheme may allow the generation of a multi-component squeezed coherent states with large mean phonon number in a fast way by choosing a suitable laser intensity, which is important in view of de-coherence processes.

A quantum key distribution protocol, based on the quantum dense encoding in entangled states, is presented. In this protocol, we introduce an encoding process to encode,two classical bits information into one of the four one-qubit unitary operations implemented by Alice and the Bell states measurement implemented by Bob in stead of direct measuring the previously shared Einstein-Podolsky-Rosen pairs by both of the distant parties, Alice and Bob Considering the practical application we can get the conclusion that our protocol has some advantages. It not only simplifies the measurement which may induce potential errors, but also improves the effectively transmitted rate of the generated qubits by the raw key. Here we also discuss eavesdropping attacks against the scheme and the channel loss.

Tunneling dynamics of multi-atomic molecules between any two multi-atomic molecular Bose-Einstein condensates with Feshbach resonance is investigated. It is indicated that the tunneling in the two Bose-Einstein condensates depends not only on the inter-molecular nonlinear interactions and the initial number of molecule in these condensates, but also on the tunneling coupling between them. It is discovered that besides oscillating tunneling current between the multi-atomic molecular condensates, the nonlinear multi-atomic molecular tunneling dynamics sustains a self-locked population imbalance: a macroscopic quantum self-trapping effect. The influence of de-coherence caused by non-condensate molecule on the tunneling dynamics is studied. It is shown that de-coherence suppresses the multi-atomic molecular tunneling.

We study tunneling dynamics of atomic group in two-species molecular Bose-Einstein condensates. It is shown that the tunneling of the atom group depends on not only the tunneling coupling constant between the atomic pair molecular condensate and the three-atomic group molecular condensate, but also the inter-molecular nonlinear interactions and the initial number of atoms in these condensates. It is discovered that besides oscillating tunneling current between the atomic pair molecular condensate and the three-atomic group molecular condensate, the nonlinear atomic group tunneling dynamics sustains a self-maintained population imbalance: a macroscopic quantum self-trapping effect.

In light of the recent experimental observation of Bose–Einstein condensates held in 1D, 2D and 3D optical lattice potentials, we derive several families of exact solutions of the Gross–Pitaevskii equation from some balance conditions between the optical potentials and interaction energies. The exact solutions in same dimension possess same norm but different phases, which describe the condensed atoms with same spatial distribution and average number of atoms per well but different transport velocities and atomic current densities.

By using Husimi's test-function method, we construct n exact solutions of a single Paul trapped ion modelled by a quantum harmonic oscillator with a time-dependent 'spring constant'. Any nth solution is a combination of the Fock state and coherent state, which describes a wavepacket train consisting of n + 1 packets. Its centre oscillates like the classical harmonic oscillator with variable frequency, while the width and height of each packet change simultaneously. When the deformation is small, it behaves like a propagated and non-deformed train, and the large deformation is identified with breathing of the wavepacket train.

We have experimentally implemented remote state preparation (RSP) of a qubit from a hydrogen to a carbon nucleus in molecules of carbon-13 labeled chloroform $^{13}$CHCl$_{3}$ over interatomic distances using liquid-state nuclear magnetic resonance (NMR) technique. Full RSP of a special ensemble of qubits, i.e., a qubit chosen from equatorial and polar great circles on a Bloch sphere with Pati's scheme, was achieved with one cbit communication. Such a RSP scheme can be generalized to prepare a large number of qubit states and may be used in other quantum information processing and quantum computing., 10 pages,5 PS figures

A simple method is applied to calculating the isotope shifts (ISs) on 5S(1/2) --> 4D(3/2,5/2) transitions of Sr-87,88(+). First we have calculated the ISs of lower transitions on a series of alkali-like systems such as B2+, Ca+ and Ba+, which are in agreement with other works. Then the ISs on 5S(1/2) --> 4D(3/2,5/2) transitions of Sr-87,88(+), which are useful to study the Sr+ optical frequency standard, are evaluated.

It is shown that two trapped ions interacting with laser beams resonant to the first red side-band of center-of-mass mode, in Lamb Dicke regime and under rotating wave approximation, is described by a Jaynes-Cummings model. For the initial condition that the motional state of centor-of-mass mode is in vacuum state and the internal state is prepared in a coherent superposition of states, coherence and squeezing for the vibratile motion of center-of-mass mode are discussed, particularly, a "weak" coherent state and a "weak" squeezed vacuum state are obtained. Collapse and revival are also observed in this type of initial condition.

Wave-particle duality refers to quantum mechanical objects behaving as waves or particles under different physical conditions. We propose a scheme for testing the wave-particle duality by means of the hot-ion quantum computation. With an efficient controlled-NOT gate, the 'which-path' information can be obtained with the method of bichromatic field. The appearance and disappearance of interference fringes due to deletion and production of the entanglement between the observed ion and the marker are analyzed, respectively. The scheme can be regarded as both a more efficient hot-ion quantum computation one and an application of quantum computation. (C) 2002 Elsevier Science B.V. All rights reserved.

Ac-Stark shift of atom levels is caused by an ac-electromagnetic field. As an electromagnetic wave, laser light does induce ac-Stark shift. It is proved experimentally that if the light is linearly polarized, the dynamic polarizability changes with polarization direction. The polarization direction of the linearly-polarized laser is tuned by 720 degrees, and the ac-Stark shifts of the 4S(1/2), m = (+/- 1/2) -> 3D(5/2), (m = +/- 1/2) clock transitions in Ca-40(+) are measured in steps of 10 degrees. The frequency shifts change with laser polarization in a periodical manner and have values opposite to each other.

We tested wave-particle duality with the ensemble-averaged spin states of C-13 nuclei in (CHCl3)-C-13 using the spin states of H-1 nuclei as the path marker. It turns out that wave-particle duality holds when one merely measures the probability density of quantum states, and that wave- and particle-like behaviour is simultaneously observed when measuring populations and coherences in a single nuclear magnetic resonance experiment. The effects of path-marking schemes and the causes of the appearance and disappearance of wave behaviour are analysed.

Magic-angle spinning (MAS) solid state nuclear magnetic resonance (NMR) spectroscopy is shown to be a promising technique for implementing quantum computing. The theory underlying the principles of quantum computing with nuclear spin systems undergoing MAS is formulated in the framework of formalized quantum Floquet theory. The procedures for realizing state labeling, state transformation and coherence selection in Floquet space are given. It suggests that by this method, the largest number of qubits can easily surpass that achievable with other techniques. Unlike other modalities proposed for quantum computing, this method enables one to adjust the dimension of the working state space, meaning the number of qubits can be readily varied. The universality of quantum computing in Floquet space with solid state NMR is discussed and a demonstrative experimental implementation of Grover's search is given., Comment: 31 pp, 8 figs, novel platform for NMR QC implementation with comprehensive theoretical account and Grover's search demo. To appear in European Phyical Journal B

The Raman interaction of a trapped ultracold ion with two traveling wave lasers is studied analytically by series expansion technique without the need of rotating wave approximation and the limitations of both the Lamb-Dicke limit and the weak excitation regime. As an example, a scheme for the preparation of Schrodinger-cat states in such a process is proposed beyond the weak excitation regime.

The most physically interesting systems are not exactly solvable in quantum mechanics. For one-dimensional bound systems without exact solutions, we analytically and numerically find that the Rayleigh-Schrodinger perturbed series sensitively depends on an unsolvable integration, which leads to numerical instability in quantum mechanics. By using an exact formal solution of the non-homogeneous Schrodinger equation, we demonstrate the existence of analytically bound states and propose a simple scheme to truncate infinity so that the instability difficulty is avoided.

We investigate the energy spectrum for hybrid mechanical systems described by non-parity-symmetric quantum Rabi models. A set of analytical solutions in terms of the confluent Heun functions and their analytical energy spectrum are obtained. The analytical energy spectrum includes regular and exceptional parts, which are both confirmed by direct numerical simulation. The regular part is determined by the zeros of the Wronskian for a pair of analytical solutions. The exceptional part is relevant to the isolated exact solutions and its energy eigenvalues are obtained by analyzing the truncation conditions for the confluent Heun functions. By analyzing the energy eigenvalues for exceptional points, we obtain the analytical conditions for the energy-level-crossings, which correspond to two-fold energy degeneracy., 17 pages, 2 figures

in coherent state representation and in the absence of rotating wave approximation, we present an approach to solve the interaction of a trapped ultracold ion with a standing wave laser by a continued fi-action, within the Lamb-Dicke limit and the low excitation regime. it is shown that, the eigen-energies as well as the coefficients of the series of the eigenfunction can be obtained rapidly from the continued fraction.

An ultracold two-level ion which stays at its internal sound state, experiencing the standing wave of a large detuning laser in a Paul trap, has been studied in the Lamb-Dicke limit and near the weak excitation regime, with full consideration of the time dependence of the trapping potential.

We report exact solutions of the Poyatos–Cirac–Zoller quantum gate system withtwo trapped ions [Phys. Rev. Lett.81, 1322 (1998)]. It is the superposition ofentangled states among the pure states of two harmonic oscillators and describesa mixed mode involving the center-of-mass and relative motions withcommensurable frequencies. Theoretical analysis of the exact solutions showsthat for a given trapping frequency the relative motion cannot be laser-cooled.

We propose an all-quantized Jaynes-Cummings (JC) interaction between a trapped ultracold ion with a quantized radiation held. The carrier excitation gives the usual JC model in cavity QED, but the red and blue excitations will result in three-body interactions analogous to a two-mode problem in quantum optics. (C) 1998 Published by Elsevier Science B.V.

The anharmonic potential felt by a single-species ions confined in a rf quadrupole trap which results from a non-ideal trap configuration and the charge distribution of the ion cloud is studied. The rf resonance-absorption spectra are explained by a Duffing oscillator and a representation of the line-shape parameter η is derived. Forη > 0.77, the electric signals will exhibit hysteresis. The relation with the anharmonic potential is discussed.

The experimental study at Wuhan Institute of Physics and Mathematics (WIPM), Chinese Academy of Scienses (CAS) on the precision spetroscopy based on single trapped Ca+ ion is described in this paper. A single Ca+ ion is trapped in a miniature Paul trap and laser cooled to Lamb-Dicke regime, and the ion can be trapped more than 2 months. The linewidth of the 729 nm laser for probing the Ca+ 4 s 2 S 1/2-3 d 2 D 5/2 clock transition is reduced to lessthan 1 Hz by locked to a super cavity, and the 729 nm laser can be locked more than 1 month continuously. Two similar Ca + ion optical frequency standards are set up for frequency comparison. The systematic uncertainty is evaluated to be ´ 10−17 for both ftrquency standards. The frequency difference of two frequency standards is measured to be 3.0 (5.5) ´ 10−17 within 42 d. The Allan deviation for a single clock is measured to be 1×10−14 τ −1/2 with a 3-d-continuous comparison, the stability for a reaches 7 ´ 10−17 at an averaging time of 20000 s. Meanwhile, the absolute frequency of the Ca+ 4 s 2 S 1/2-3 d 2 D 5/2 clock transition is measured to be 411042129776401.7(1.1) Hz with respect to the SI second through the Global Positioning System (GPSx). The precision spectroscopy experiments are carried out based on the single Ca+ ion system. The magic wavelengths for the Ca+ optical frequency standardare measured to be λ | mj |=1/2=395.7992(7) nm and λ | mj |=3/2=395.7990(7) nm, which agrees with theoretical calculation made by Tang et al. The lifetime of the 3 d 2 D 5/2 is measured to be 1174(10) ms, which is agree with the experimental measurement made by University of Oxford and University of Innsbruck and the recent theoretical calculation made by Sahoo.