Wolfgang Rohringer, Robert Buecker, Stephanie Manz, Thomas Betz, Christian Koller, Martin Goebel, Aurelien Perrin, Joerg Schmiedmayer, Thorsten Schumm
We employ an evolutionary algorithm to automatically optimize different stages of a cold atom experiment without human intervention. This approach closes the loop between computer based experimental control systems and automatic real time analysis and can be applied to a wide range of experimental situations. The genetic algorithm quickly and reliably converges to the most performing parameter set independent of the starting population. Especially in many-dimensional or connected parameter spaces the automatic optimization outperforms a manual search.
Alex D. Gottlieb, Thorsten Schumm
Bosonic Josephson junctions can be realized by confining ultracold gases of bosons in multi-well traps, and studied theoretically with the $M$-site Bose-Hubbard model. We show that canonical equilibrium states of the $M$-site Bose-Hubbard model may be approximated by mixtures of coherent states, provided the number of atoms is large and the total energy is comparable to $k_BT$. Using this approximation, we study thermal fluctuations in bosonic Josephson junctions in the mean field regime. Statistical estimates of the fluctuations of relative phase and number, obtained by averaging over many replicates of an experiment, can be used to estimate the temperature and the tunneling parameter, or to test whether the experimental procedure is effectively sampling from a canonical thermal equilibrium ensemble.
Georgy A. Kazakov, Thorsten Schumm
We consider various approaches to the creation of a high-stability active optical frequency standard, where the atomic ensemble itself produces a highly stable and accurate frequency signal. The short-time frequency stability of such standards may overcome the stability of lasers stabilized to macroscopic cavities which are used as local oscillators in the modern optical frequency standard systems. The main idea is to create a "superradiant" laser operating deep in the bad cavity regime, where the decay rate of the cavity field significantly exceeds the decoherence rate of the lasing transition. Two main approaches towards the realization of an active optical frequency standard have been proposed already: the optical lattice laser, and the atomic beam laser. We consider these and some alternative approaches, and discuss the parameters for atomic ensembles necessary to attain the metrology relevant level of short-time frequency stability, and various effects and main challenges critical for practical implementations.
Martin Trinker, Sönke Groth, Stefan Haslinger, Stephanie Manz, Thomas Betz, Israel Bar-Joseph, Thorsten Schumm, Jörg Schmiedmayer
We employ a combination of optical UV- and electron-beam-lithography to create an atom chip combining sub-micron wire structures with larger conventional wires on a single substrate. The new multi-layer fabrication enables crossed wire configurations, greatly enhancing the flexibility in designing potentials for ultra cold quantum gases and Bose-Einstein condensates. Large current densities of >6 x 10^7 A/cm^2 and high voltages of up to 65 V across 0.3 micron gaps are supported by even the smallest wire structures. We experimentally demonstrate the flexibility of the next generation atom chip by producing Bose-Einstein condensates in magnetic traps created by a combination of wires involving all different fabrication methods and structure sizes.
David A. Smith, Simon Aigner, Sebastian Hofferberth, Michael Gring, Mauritz Andersson, Stefan Wildermuth, Peter Krüger, Stephan Schneider, Thorsten Schumm, Jörg Schmiedmayer
Imaging ultracold atomic gases close to surfaces is an important tool for the detailed analysis of experiments carried out using atom chips. We describe the critical factors that need be considered, especially when the imaging beam is purposely reflected from the surface. In particular we present methods to measure the atom-surface distance, which is a prerequisite for magnetic field imaging and studies of atom surface-interactions.
Kjeld Beeks, Tomas Sikorsky, Veronika Rosecker, Martin Pressler, Fabian Schaden, David Werban, Niyusha Hosseini, Lukas Rudischer, Felix Schneider, Patrick Berwian, Jochen Friedrich, Dieter Hainz, Jan Welch, Johannes H. Sterba, Georgy Kazakov, Thorsten Schumm
We have grown $^{232}$Th:CaF$_2$ and $^{229}$Th:CaF$_2$ single crystals for investigations on the VUV laser-accessible first nuclear excited state of $^{229}$Th. To reach high doping concentrations despite the extreme scarcity (and radioactivity) of $^{229}$Th, we have scaled down the crystal volume by a factor 100 compared to established commercial or scientific growth processes. We use the vertical gradient freeze method on 3.2 mm diameter seed single crystals with a 2 mm drilled pocket, filled with a co-precipitated CaF$_2$:ThF$_4$:PbF$_2$ powder in order to grow single crystals. Concentrations of $4\cdot10^{19}$ cm$^{-3}$ have been realized with $^{232}$Th with good ($>$10%) VUV transmission. However, the intrinsic radioactivity of $^{229}$Th drives radio-induced dissociation during growth and radiation damage after solidification. Both lead to a degradation of VUV transmission, limiting the $^{229}$Th concentration to $<5\cdot10^{17}$ cm$^{-3}$.
Marcius H. T. Extavour, Lindsay J. LeBlanc, Jason McKeever, Alma B. Bardon, Seth Aubin, Stefan Myrskog, Thorsten Schumm, Joseph H. Thywissen
Nov 10, 2008·quant-ph·PDF We review our recent and ongoing work with Fermi gases on an atom chip. After reviewing some statistical and thermodynamic properties of the ideal, non-interacting Fermi gas, and a brief description of our atom chip and its capabilities, we discuss our experimental approach to producing a potassium-40 degenerate Fermi gas (DFG) using sympathetic cooling by a rubidium-87 Bose-Einstein condensate on an atom chip. In doing so, we describe the factors affecting the loading efficiency of the atom chip microtrap. This is followed by a discussion of species selectivity in radio frequency manipulation of the Bose-Fermi mixture, which we explore in the context of sympathetic evaporative cooling and radio-frequency dressed adiabatic double-well potentials. Next, we describe the incorporation of a crossed-beam dipole trap into the atom chip setup, in which we generate and manipulate strongly interacting spin mixtures of potassium-40. Finally, we conclude with a brief discussion of future research directions with DFGs and atom chips.
Brenden S. Nickerson, Martin Pimon, Pavlo V. Bilous, Johannes Gugler, Georgy A. Kazakov, Tomas Sikorsky, Kjeld Beeks, Andreas Gruneis, Thorsten Schumm, Adriana Palffy
The electronic defect states resulting from doping $^{229}$Th in CaF$_2$ offer a unique opportunity to excite the nuclear isomeric state $^{229m}$Th at approximately 8 eV via electronic bridge mechanisms. We consider bridge schemes involving stimulated emission and absorption using an optical laser. The role of different multipole contributions, both for the emitted or absorbed photon and nuclear transition, to the total bridge rates are investigated theoretically. We show that the electric dipole component is dominant for the electronic bridge photon. In contradistinction, the electric quadrupole channel of the $^{229}$Th isomeric transition plays the dominant role for the bridge processes presented. The driven bridge rates are discussed in the context of background signals in the crystal environment and of implementation methods. We show that inverse electronic bridge processes quenching the isomeric state population can improve the performance of a solid-state nuclear clock based on $^{229m}$Th.
Jerome Esteve, Thorsten Schumm, Jean-Baptiste Trebbia, Isabelle Bouchoule, Alain Aspect, Christopher Westbrook
We discuss design considerations and the realization of a magnetic double-well potential on an atom chip using current-carrying wires. Stability requirements for the trapping potential lead to a typical size of order microns for such a device. We also present experiments using the device to manipulate cold, trapped atoms.
Georgy A. Kazakov, Thorsten Schumm
It has been proposed to use magnetically trapped atomic ensembles to enhance the interrogation time in microwave clocks. To mitigate the perturbing effects of the magnetic trap, near-magic-field configurations are employed, where the involved clock transition becomes independent of the atom's potential energy to first order. Still, higher order effects are a dominating source for dephasing, limiting the performance of this approach. Here we propose a simple method to cancel the energy dependence to both first and second order, using weak radio-frequency dressing. We give values for dressing frequencies, amplitudes, and trapping fields for 87Rb atoms and investigate quantitatively the robustness of these second-order-magic conditions to variations of the system parameters. We conclude that radio-frequency dressing can suppress field-induced dephasing by at least one order of magnitude for typical experimental parameters
Chuankun Zhang, Tian Ooi, Jacob S. Higgins, Jack F. Doyle, Lars von der Wense, Kjeld Beeks, Adrian Leitner, Georgy Kazakov, Peng Li, Peter G. Thirolf, Thorsten Schumm, Jun Ye
Optical atomic clocks$^{1,2}$ use electronic energy levels to precisely keep track of time. A clock based on nuclear energy levels promises a next-generation platform for precision metrology and fundamental physics studies. Thorium-229 nuclei exhibit a uniquely low energy nuclear transition within reach of state-of-the-art vacuum ultraviolet (VUV) laser light sources and have therefore been proposed for construction of the first nuclear clock$^{3,4}$. However, quantum state-resolved spectroscopy of the $^{229m}$Th isomer to determine the underlying nuclear structure and establish a direct frequency connection with existing atomic clocks has yet to be performed. Here, we use a VUV frequency comb to directly excite the narrow $^{229}$Th nuclear clock transition in a solid-state CaF$_2$ host material and determine the absolute transition frequency. We stabilize the fundamental frequency comb to the JILA $^{87}$Sr clock$^2$ and coherently upconvert the fundamental to its 7th harmonic in the VUV range using a femtosecond enhancement cavity. This VUV comb establishes a frequency link between nuclear and electronic energy levels and allows us to directly measure the frequency ratio of the $^{229}$Th nuclear clock transition and the $^{87}$Sr atomic clock. We also precisely measure the nuclear quadrupole splittings and extract intrinsic properties of the isomer. These results mark the start of nuclear-based solid-state optical clock and demonstrate the first comparison of nuclear and atomic clocks for fundamental physics studies. This work represents a confluence of precision metrology, ultrafast strong field physics, nuclear physics, and fundamental physics.
Robert Bücker, Tarik Berrada, Sandrine van Frank, Jean-François Schaff, Thorsten Schumm, Jörg Schmiedmayer, Georg Jäger, Julian Grond, Ulrich Hohenester
We present theoretical and experimental results on high-fidelity transfer of a trapped Bose-Einstein condensate into its first vibrationally excited eigenstate. The excitation is driven by mechanical motion of the trap, along a trajectory obtained from optimal control theory. Excellent agreement between theory and experiment is found over a large range of parameters. We develop an approximate model to map the dynamics of the many-body condensate wave function to a driven two-level system.
Georg Jäger, Tarik Berrada, Jörg Schmiedmayer, Thorsten Schumm, Ulrich Hohenester
Nov 10, 2015·quant-ph·PDF We theoretically investigate the creation of squeezed states of a Bose-Einstein Condensate (BEC) trapped in a magnetic double well potential. The number or phase squeezed states are created by modulating the tunnel coupling between the two wells periodically with twice the Josephson frequency, i.e., through parametric amplification. Simulations are performed with the multi configurational Hartree method for bosons (MCTDHB). We employ optimal control theory to bring the condensate to a complete halt at a final time, thus creating a highly squeezed state (squeezing factor of 0.12, $ξ_S^2=-18$ dB) suitable for atom interferometry.
Simon Stellmer, Matthias Schreitl, Georgy Kazakov, Johannes Sterba, Thorsten Schumm
We propose a simple approach to measure the energy of the few-eV isomeric state in Th-229. To this end, U-229 nuclei are doped into VUV-transparent crystals, where they undergo alpha decay into Th-229, and, with a probability of 2%, populate the isomeric state. These Th-229m nuclei may decay into the nuclear ground state under emission of the sought-after VUV gamma, whose wavelength can be determined with a spectrometer. Based on measurements of the optical transmission of U:CaF2 crystals in the VUV range, we expect a signal at least 2 orders of magnitude larger compared to current schemes using surface-implantation of recoil nuclei. The signal background is dominated by Cherenkov radiation induced by beta decays of the thorium decay chain. We estimate that, even if the isomer undergoes radiative de-excitation with a probability of only 0.1%, the VUV gamma can be detected within a reasonable measurement time.
Kamil Nalikowski, Valera Veryazov, Kjeld Beeks, Thorsten Schumm, Marek Krosnicki
Building on recent advances of the embedded cluster approach combined with multiconfigurational theory, this work investigates the electronic states in thorium-doped CaF2 crystals. Th:CaF2 is currently establishing as a promising material for solid-state nuclear clocks, which utilize the laser-accessible isomeric state in thorium-229. By comparing simulated absorption spectra of a library of defect configurations with experimental data, we demonstrate the impact of fluorine vacancies and calcium vacancies on the Th:CaF2 electronic structure. Our results indicate that fluorine-deficient sites can introduce local electronic states within the band gap, resonant with the isomer energy, potentially contributing to non-radiative decay or quenching of the Th-229 isomer. We also explore the potential of electron-nuclear bridge mechanisms to enhance nuclear excitation or de-excitation, offering a pathway for more efficient control over the nuclear clock. This study provides key insights for optimizing the crystal environment for nuclear metrology applications and opens new avenues for further experimental and theoretical exploration of thorium-doped ionic crystals.
Kjeld Beeks, Georgy A. Kazakov, Fabian Schaden, Ira Morawetz, Luca Toscani de Col, Thomas Riebner, Michael Bartokos, Tomas Sikorsky, Thorsten Schumm, Chuankun Zhang, Tian Ooi, Jacob S. Higgins, Jack F. Doyle, Jun Ye, Marianna S. Safronova
State-resolved laser spectroscopy at the 10$^{-12}$ precision level recently reported in $arXiv$:2406.18719 determined the fractional change in nuclear quadrupole moment between the ground and isomeric state of $^{229}\rm{Th}$, $ΔQ_0/Q_0$=1.791(2) %. Assuming a prolate spheroid nucleus, this allows to quantify the sensitivity of the nuclear transition frequency to variations of the fine-structure constant $α$ to $K=5900(2300)$, with the uncertainty dominated by the experimentally measured charge radius difference $Δ\langle r^2 \rangle$ between the ground and isomeric state. This result indicates a three orders of magnitude enhancement over atomic clock schemes based on electron shell transitions. We find that $ΔQ_0$ is highly sensitive to tiny changes in the nuclear volume, thus the constant volume approximation cannot be used to accurately relate changes in $\langle r^2 \rangle$ and $Q_0$. The difference between the experimental and estimated values in $ΔQ_0/Q_0$ raises a further question on the octupole contribution to the alpha-sensitivity.
Martin Pimon, Tobias Kirschbaum, Thorsten Schumm, Adriana Pálffy, Andreas Grüneis
Thorium-doped LiCaAlF$_6$ and LiSrAlF$_6$ (Th:LiCAF and Th:LiSAF) are promising crystals for a solid-state nuclear clock based on the 8 eV transition in $^{229}$Th; however, their complex crystal structures complicate understanding the atomic arrangement of the thorium defects. In this work, density functional theory simulations are employed to systematically investigate these systems, including temperature-dependent effects and environmental conditions of fluorine saturation and deficiency. We investigated 20 distinct charge compensation schemes for each material, revealing lower defect formation energies in Th:LiSAF than in Th:LiCAF. This suggests that the former may attain a higher concentration of thorium nuclei. Furthermore, we calculated the electric field gradient for the lowest energy structure per compensation pathway. Our investigation shows that results previously reported in the literature apply only to a subset of experimental conditions.
Thomas Betz, Stephanie Manz, Robert Bücker, Tarik Berrada, Christian Koller, Georgy Kazakov, Igor E. Mazets, Hans-Peter Stimming, Aurelien Perrin, Thorsten Schumm, Jörg Schmiedmayer
We realize a one-dimensional Josephson junction using quantum degenerate Bose gases in a tunable double well potential on an atom chip. Matter wave interferometry gives direct access to the relative phase field, which reflects the interplay of thermally driven fluctuations and phase locking due to tunneling. The thermal equilibrium state is characterized by probing the full statistical distribution function of the two-point phase correlation. Comparison to a stochastic model allows to measure the coupling strength and temperature and hence a full characterization of the system.
Robert Bücker, Ulrich Hohenester, Tarik Berrada, Sandrine van Frank, Aurélien Perrin, Stephanie Manz, Thomas Betz, Julian Grond, Thorsten Schumm, Jörg Schmiedmayer
We develop a model for parametric amplification, based on a density matrix approach, which naturally accounts for the peculiarities arising for matter waves: significant depletion and explicit time-dependence of the source state population, long interaction times, and spatial dynamics of the amplified modes. We apply our model to explain the details in an experimental study on twin-atom beam emission from a one-dimensional degenerate Bose gas.
Georgy A. Kazakov, Thorsten Schumm
Recently, several theoretical proposals adressed the generation of an active optical frequency standard based on atomic ensembles trapped in an optical lattice potential inside an optical resonator. Using atoms with a narrow linewidth transition and population inversion together with a "bad" cavity allows to the realize the superradiant photon emission regime. These schemes reduce the influence of mechanical or thermal vibrations of the cavity mirrors on the emitted optical frequency, overcoming current limitation in passive optical standards. The coherence time of the emitted light is ultimately limited by the lifetime of the atoms in the optical lattice potential. Therefore these schemes would produce one light pulse per atomic ensemble without a phase relation between pulses. Here we study how phase coherence between pulses can be maintained by using several inverted atomic ensenbles, introduced into the cavity sequentially by means of a transport mechanism. We simulate the light emission process using the Heisenberg-Langevin approach and study the frequency noise of the intracavity field.