Clock States Research Articles

Dispersive detection of radio-frequency-dressed states

We introduce a method to dispersively detect alkali atoms in radio-frequency dressed states. In particular, we use dressed detection to measure populations and population differences of atoms prepared in their clock states. Linear birefringence of the atomic medium enables atom number detection via polarisation homodyning, a form of common path interferometry. In order to achieve low technical noise levels, we perform optical sideband detection after adiabatic transformation of bare states into dressed states. The balanced homodyne signal then oscillates independently of field fluctuations at twice the dressing frequency, thus allowing for robust, phase-locked detection that circumvents low-frequency noise. Using probe pulses of two optical frequencies, we can detect both clock states simultaneously and obtain population difference as well as the total atom number. The scheme also allows for difference measurements by direct subtraction of the homodyne signals at the balanced detector, which should technically enable quantum noise limited measurements with prospects for the preparation of spin squeezed states. The method extends to other Zeeman sublevels and can be employed in a range of atomic clock schemes, atom interferometers, and other experiments using dressed atoms.

Polaronic and dressed molecular states in orbital Feshbach resonances

We consider the impurity problem in an orbital Feshbach resonance (OFR), with a single excited clock state $|e\uparrow\rangle$ atom immersed in a Fermi sea of electronic ground state $|g\downarrow\rangle$. We calculate the polaron effective mass and quasi-particle residue, as well as the polaron to molecule transition. By including one particle-hole excitation in the molecular state, we find significant correction to the transition point. This transition point moves toward the BCS side for increasing particle densities, which suggests that the corresponding many-body physics is similar to a narrow resonance.

Experimental Determination of the Landé g-Factors for 5s2 1S and 5s5p 3P States of the 87Sr Atom**Supported by the National Natural Science Foundation of China under Grant Nos 61127901, 11404025 and 91536106, the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No XDB21030700, the Key Research Project of Frontier Science of Chinese Academy of Sciences under

We present an experimental determination on the Landé g-factors for the 5s2 1S0 and 5s5p 3P0 states in ultra-cold atomic systems, which is important for evaluating the Zeeman shift of the clock transition in the 87Sr optical lattice clock. The Zeeman shift of the 5s5p 3P0–5s2 1S0 forbidden transition is measured with the π-polarized and σ±-polarized interrogations at different magnetic field strengths. Moreover, in the g-factor measurement with the σ±-transition spectra, it is unnecessary to calibrate the external magnetic field. By this means, the ground state 5s2 1S0 g-factor for the 87Sr atom is −1.306(52)×10−4, which is the first experimental determination to the best of our knowledge, and the result matches very well with the theoretical estimation. The differential g-factor δg between the 5s5p 3P0 state and the 5s2 1S0 state of the 87Sr atoms is measured in the experiment as well, which are −7.67(36) × 10−5 with π-transition spectra and −7.72(43) × 10−5 with σ±-transition spectra, in good agreement with the previous report [Phys. Rev. A 76 (2007) 022510]. This work can also be used for determining the differential g-factor of the clock states for the optical clocks based on other atoms.

Optical-plus-microwave pumping in a magnetically insensitive state of cold atoms

An optical-plus-microwave pumping method is implemented and optimized to pump cold atoms to a magnetically insensitive state in an integrating sphere. This method consists of several optical and microwave pulses with a proper time sequence. The relative population of cold atoms in the Zeeman sublevel $|F=1,{m}_{F}=0\ensuremath{\rangle}$ is tested by measuring the Rabi oscillations and Ramsey fringes with different numbers of optical and microwave pumping pulses, demonstrating that nearly 83% of the cold atoms can be prepared in the clock state. The number of cold atoms in the target state is up to 2.5 times more than that of the optical pumping alone. Thus, the limitation on the stability of an integrating sphere cold-atom clock from atomic noise is estimated to be from $4.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$ to $3.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1/2}$. This method is also suitable for other precision measurements with cold atoms.

Multipolar Polarizabilities and Hyperpolarizabilities in the Sr Optical Lattice Clock.

We address the problem of the lattice Stark shifts in the Sr clock caused by the multipolar M1 and E2 atom-field interactions and by the term nonlinear in lattice intensity and determined by the hyperpolarizability. We develop an approach to calculate hyperpolarizabilities for atoms and ions based on a solution of the inhomogeneous equation which allows us to effectively and accurately carry out complete summations over intermediate states. We apply our method to the calculation of the hyperpolarizabilities for the clock states in Sr. We also carry out an accurate calculation of the multipolar polarizabilities for these states at the magic frequency. Understanding these Stark shifts in optical lattice clocks is crucial for further improvement of the clock accuracy.

Dynamics of interacting fermions under spin–orbit coupling in an optical lattice clock

Quantum statistics and symmetrization dictate that identical fermions do not interact via s-wave collisions. However, in the presence of spin-orbit coupling (SOC), fermions prepared in identical internal states with distinct momenta become distinguishable. The resulting strongly interacting system can exhibit exotic topological and pairing behaviors, many of which are yet to be observed in condensed matter systems. Ultracold atomic gases offer a promising pathway for simulating these rich phenomena. Two recent experiments reported the observation of single atom SOC in optical lattice clocks (OLCs) based on alkaline-earth atoms. In these works encoding the effective spin degree of freedom in the long-lived electronic clock states significantly reduced the detrimental effects of spontaneous emission and heating that have thus far hindered the study of interacting SOC with alkali atoms. Beyond first studies of interacting SOC with alkali atoms in a bulk gas and with two particles in a lattice, here we enter a new regime of many-body interacting SOC in an OLC. Using clock spectroscopy, we observe the precession of the collective magnetization and the emergence of spin locking effects arising from an interplay between p-wave and SOC-induced exchange interactions. The many-body dynamics are well captured by a collective XXZ spin model, which describes a broad class of condensed matter systems ranging from superconductors to quantum magnets. Furthermore, our work will aid in the design of next-generation OLCs by offering a route for avoiding the observed large density shifts caused by SOC-induced exchange interactions.

Enhancing Kondo coupling in alkaline-earth-metal atomic gases with confinement-induced resonances in mixed dimensions

The Kondo effect describes the spin-exchanging interaction between localized impurity and the itinerant fermions. The ultracold alkaline-earth atomic gas provides a natural platform for quantum simulation of the Kondo model, utilizing its long-lived clock state and the nuclear-spin exchanging interaction between the clock state and the ground state. One of the key issue now is whether the Kondo temperature can be high enough to be reached in current experiment, for which we have proposed using a transverse confinement to confine atoms into a one-dimensional tube and to utilize the confinement-induced resonance to enhance the Kondo coupling. In this work, we further consider the $1+0$ dimensional scattering problem when the clock state is further confined by an axial harmonic confinement. We show that this axial confinement for the clock state atoms not only plays a role for localizing them, but also can act as an additional control knob to reach the confinement-induced resonance. We show that by combining both the transverse and the axial confinements, the confinement-induced resonance can be reached in the practical conditions and the Kondo effect can be attainable in this system.

Symmetry-Protected Topological States for Interacting Fermions in Alkaline-Earth-Like Atoms.

We discuss the quantum simulation of symmetry-protected topological (SPT) states for interacting fermions in quasi-one-dimensional gases of alkaline-earth-like atoms such as ^{173}Yb. Taking advantage of the separation of orbital and nuclear-spin degrees of freedom in these atoms, we consider Raman-assisted spin-orbit couplings in the clock states, which, together with the spin-exchange interactions in the clock-state manifolds, give rise to SPT states for interacting fermions. We numerically investigate the phase diagram of the system, and study the phase transitions between the SPT phase and the symmetry-breaking phases. The interaction-driven topological phase transition can be probed by measuring local density distribution of the topological edge modes.

Clock spectroscopy of interacting bosons in deep optical lattices

We report on high-resolution optical spectroscopy of interacting bosonic 174Yb atoms in deep optical lattices with negligible tunneling. We prepare Mott insulator phases with singly- and doubly-occupied isolated sites and probe the atoms using an ultra-narrow ‘clock’ transition. Atoms in singly-occupied sites undergo long-lived Rabi oscillations. Atoms in doubly-occupied sites are strongly affected by interatomic interactions, and we measure their inelastic decay rates and energy shifts. We deduce from these measurements all relevant collisional parameters involving both clock states, in particular the intra- and inter-state scattering lengths.

Universal interrogation protocol with zero probe-field-induced frequency shift for quantum clocks and high-accuracy spectroscopy

Optical clock interrogation protocols, based on laser-pulse spectroscopy, suffer from probe-induced frequency shifts and their variations induced by laser power. The original hyper-Ramsey probing scheme, which was proposed to alleviate those issues, does not fully eliminate the shift, especially when decoherence and relaxation by spontaneous emission or collisions are present. We propose to solve the fundamental problem of frequency shifts induced by the laser probe by deriving the exact canonical form of a multipulse generalized hyper-Ramsey resonance, including decoherence and relaxation. We present a universal interrogation protocol based on composite laser-pulse spectroscopy with phase modulation eliminating probe-induced frequency shifts at all orders in the presence of various dissipative processes. Unlike frequency shift extrapolation based methods, a universal interrogation protocol based on $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/4$ and $\ifmmode\pm\else\textpm\fi{}3\ensuremath{\pi}/4$ phase-modulated resonances is proposed which does not compromise the stability of the optical clock while maintaining an ultrarobust error signal gradient in the presence of substantial uncompensated ac Stark shifts. Such a scheme can be implemented in two flavors: either by inverting clock state initialization or by pulse order reversal even without a perfect quantum state initialization. This universal interrogation protocol can be applied to atomic, molecular, and nuclear frequency metrology, mass spectrometry, and the field of precision spectroscopy. It might be designed using magic-wave-induced transitions, two-photon excitation, and magnetically induced spectroscopy or it might even be implemented with quantum logic gate circuit and qubit entanglement.

Hyperfine-mediated electric quadrupole shifts inAl+andIn+ion clocks

We evaluate the electric quadrupole moments of the ${^1}\!S_0$ and ${^3}\!P_0$ clock states of $^{27}$Al$^+$ and $^{115}$In$^+$. To capture all dominant contributions, our analysis extends through third order of perturbation theory and includes hyperfine coupling of the electrons to both the magnetic dipole and electric quadrupole moments of the nucleus. For $^{27}$Al$^+$, a fortuitous cancellation leads to a suppressed frequency shift. This should allow for continued improvement of the clock without special techniques to control or cancel the shift, such as the averaging schemes that are critical to other optical ion clocks.

Spin-orbit-coupled fermions in an optical lattice clock.

Engineered spin-orbit coupling (SOC) in cold-atom systems can enable the study of new synthetic materials and complex condensed matter phenomena. However, spontaneous emission in alkali-atom spin-orbit-coupled systems is hindered by heating, limiting the observation of many-body effects and motivating research into potential alternatives. Here we demonstrate that spin-orbit-coupled fermions can be engineered to occur naturally in a one-dimensional optical lattice clock. In contrast to previous SOC experiments, here the SOC is both generated and probed using a direct ultra-narrow optical clock transition between two electronic orbital states in 87Sr atoms. We use clock spectroscopy to prepare lattice band populations, internal electronic states and quasi-momenta, and to produce spin-orbit-coupled dynamics. The exceptionally long lifetime of the excited clock state (160 seconds) eliminates decoherence and atom loss from spontaneous emission at all relevant experimental timescales, allowing subsequent momentum- and spin-resolved in situ probing of the SOC band structure and eigenstates. We use these capabilities to study Bloch oscillations, spin-momentum locking and Van Hove singularities in the transition density of states. Our results lay the groundwork for using fermionic optical lattice clocks to probe new phases of matter.

Circadian Oscillations of NADH Redox State Using a Heterologous Metabolic Sensor in Mammalian Cells

It is known that there are mechanistic links between circadian clocks and metabolic cycles. Reduced nicotinamide adenine dinucleotide (NADH) is a key metabolic cofactor in all living cells; however, it is not known whether levels of NADH oscillate or not. Here we employed REX, a bacterial NADH-binding protein, fused to the VP16 activator to convert intracellular endogenous redox balance into transcriptional readouts by a reporter gene in mammalian cells. EMSA results show that the DNA binding activity of both T- and S-REX::VP16 fusions is decreased with a reduced-to-oxidized cofactor ratio increase. Transient and stabilized cell lines bearing the REX::VP16 and the REX binding operator (ROP) exhibit two circadian luminescence cycles. Consistent with these results, NADH oscillations are observed in host cells, indicating REX can act as a NADH sensor to report intracellular dynamic redox homeostasis in mammalian cells in real time. NADH oscillations provide another metabolic signal for coupling the circadian clock and cellular metabolic states.

Simplified ultra-tightly coupled BDS/INS integrated navigation system

Due to advantages such as low cost, small size, low weight, low power consumption, powerful capability of anti-jamming, and high dynamics, ultra-tightly coupled GNSS/MIMU integrated navigation systems are extensively used in projectile and precision-guided munitions. To overcome the nonlinearity of baseband signal processing and the complexity of the navigation filter, in this paper, we design a novel architecture for the ultra-tightly coupled (UTC) Beidou navigation satellite system (BDS)/INS integration based on the BDS B3 signal, including the combination of code phase and carrier phase dynamics baseband prefilter model, and the navigation filter navigation error propagation and measurement models. To eliminate the clock state components, i.e., the receiver clock offset and clock drift, the pseudorange, delta pseudorange, and delta pseudorange rate residuals obtained from baseband signal prefilters are differenced between two satellites. Based on the BDS/INS simulator, a test system for the UTC BDS/INS integrated navigation system is developed and UTC performance is evaluated. Some preliminary conclusions are formed about the effectiveness of the UTC BDS/INS integration approach.

Engineering large Stark shifts for control of individual clock state qubits

In quantum information science, the external control of qubits must be balanced with the extreme isolation of the qubits from the environment. Atomic qubit systems typically mitigate this balance through the use of gated laser fields that can create superpositions and entanglement between qubits. Here we propose the use of high-order optical Stark shifts from optical fields to manipulate the splitting of atomic qubits that are insensitive to other types of fields. We demonstrate a fourth-order AC Stark shift in a trapped atomic ion system that does not require extra laser power beyond that needed for other control fields. We individually address a chain of tightly-spaced trapped ions and show how these controlled shifts can produce an arbitrary product state of ten ions as well as generate site-specific magnetic field terms in a simulated spin Hamiltonian.

Large energy superpositions via Rydberg dressing

We propose to create superposition states of over 100 Strontium atoms being in a ground state or metastable optical clock state, using the Kerr-type interaction due to Rydberg state dressing in an optical lattice. The two components of the superposition can differ by of order 300 eV in energy, allowing tests of energy decoherence models with greatly improved sensitivity. We take into account the effects of higher-order nonlinearities, spatial inhomogeneity of the interaction, decay from the Rydberg state, collective many-body decoherence, atomic motion, molecular formation and diminishing Rydberg level separation for increasing principal number.

The core clock gene Per1 phases molecular and electrical circadian rhythms in SCN neurons.

The brain’s biological clock, the suprachiasmatic nucleus (SCN), exhibits endogenous 24-hour rhythms in gene expression and spontaneous firing rate; however, the functional relationship between these neuronal rhythms is not fully understood. Here, we used a Per1::GFP transgenic mouse line that allows for the simultaneous quantification of molecular clock state and firing rate in SCN neurons to examine the relationship between these key components of the circadian clock. We find that there is a stable, phased relationship between E-box-driven clock gene expression and spontaneous firing rate in SCN neurons and that these relationships are independent of light input onto the system or of GABAA receptor-mediated synaptic activity. Importantly, the concordant phasing of gene and neural rhythms is disrupted in the absence of the homologous clock gene Per1, but persists in the absence of the core clock gene Per2. These results suggest that Per1 plays a unique, non-redundant role in phasing gene expression and firing rate rhythms in SCN neurons to increase the robustness of cellular timekeeping.

Costs of Clock-Environment Misalignment in Individual Cyanobacterial Cells

Circadian rhythms are endogenously generated daily oscillations in physiology that are found in all kingdoms of life. Experimental studies have shown that the fitness of Synechococcus elongatus, a photosynthetic microorganism, is severely affected in non-24-h environments. However, it has been difficult to study the effects of clock-environment mismatch on cellular physiology because such measurements require a precise determination of both clock state and growth rate in the same cell. Here, we designed a microscopy platform that allows us to expose cyanobacterial cells to pulses of light and dark while quantitatively measuring their growth, division rate, and circadian clock state over many days. Our measurements reveal that decreased fitness can result from a catastrophic growth arrest caused by unexpected darkness in a small subset of cells with incorrect clock times corresponding to the subjective morning. We find that the clock generates rhythms in the instantaneous growth rate of the cell, and that the time of darkness vulnerability coincides with the time of most rapid growth. Thus, the clock mediates a fundamental trade-off between growth and starvation tolerance in cycling environments. By measuring the response of the circadian rhythm to dark pulses of varying lengths, we constrain a mathematical model of a population’s fitness under arbitrary light/dark schedules. This model predicts that the circadian clock is only advantageous in highly regular cycling environments with frequencies sufficiently close to the natural frequency of the clock.

Raman transitions between hyperfine clock states in a magnetic trap

We present our experimental investigation of an optical Raman transition between the magnetic clock states of $^{87}$Rb in an atom chip magnetic trap. The transfer of atomic population is induced by a pair of diode lasers which couple the two clock states off-resonantly to an intermediate state manifold. This transition is subject to destructive interference of two excitation paths, which leads to a reduction of the effective two-photon Rabi-frequency. Furthermore, we find that the transition frequency is highly sensitive to the intensity ratio of the diode lasers. Our results are well described in terms of light shifts in the multi-level structure of $^{87}$Rb. The differential light shifts vanish at an optimal intensity ratio, which we observe as a narrowing of the transition linewidth. We also observe the temporal dynamics of the population transfer and find good agreement with a model based on the system's master equation and a Gaussian laser beam profile. Finally, we identify several sources of decoherence in our system, and discuss possible improvements.

Possibility of triple magic trapping of clock and Rydberg states of divalent atoms in optical lattices

We predict the possibility of ‘triply magic’ optical lattice trapping of neutral divalent atoms. In such a lattice, the and clock states and an additional Rydberg state experience identical optical potentials, fully mitigating detrimental effects of the motional decoherence. In particular, we show that this triply magic trapping condition can be satisfied for Yb atom at optical wavelengths and for various other divalent systems (Ca, Mg, Hg and Sr) in the UV region. We assess the quality of triple magic trapping conditions by estimating the probability of excitation out of the motional ground state as a result of the excitations between the clock and the Rydberg states. We also calculate trapping laser-induced photoionization rates of divalent Rydberg atoms at magic frequencies. We find that such rates are below the radiative spontaneous-emission rates, due to the presence of Cooper minima in photoionization cross-sections.