Quantum entanglement between an atom and a molecule

Quantum state tracking and control of a single molecular ion in a thermal environment

Understanding molecular state evolution is central to many disciplines, including molecular dynamics, precision measurement, and molecule-based quantum technology. Details of this evolution are obscured when observing a statistical ensemble of molecules. Here, we report real-time observations of thermal radiation-driven transitions between individual states ("jumps") of a single molecule. We reversed these jumps through microwave-driven transitions, which resulted in a 20-fold improvement in the time the molecule dwells in a chosen state. The measured transition rates showed anisotropy in the thermal environment, pointing to the possibility of using single molecules as in situ probes for the strengths of ambient fields. Our approaches for state detection and manipulation could apply to a wide range of species, facilitating their uses in fields including quantum science, molecular physics, and ion-neutral chemistry.

Photodissociation spectra of single trapped CaOH+ molecular ions

Molecular ions that are generated by chemical reactions with trapped atomic ions can serve as an accessible testbed for developing molecular quantum technologies. On the other hand, they are also a hindrance to scaling up quantum computers based on atomic ions, as unavoidable reactions with background gases destroy the information carriers. Here, we investigate the single- and two-photon dissociation processes of single CaOH+ molecular ions co-trapped in Ca+ ion crystals using a femtosecond laser system. We report the photodissociation cross section spectra of CaOH+ for single-photon processes at λ = 245-275 nm and for two-photon processes at λ = 500-540 nm. Measurements are interpreted with quantum-chemical calculations, which predict the photodissociation threshold for CaOH+ → Ca+ + OH at 265 nm. This result can serve as a basis for dissociation-based spectroscopy for studying the internal structure of CaOH+. The result also gives a prescription for recycling Ca+ ions in large-scale trapped Ca+ quantum experiments from undesired CaOH+ ions formed in the presence of background water vapor.

Opportunities for fundamental physics research with radioactive molecules

Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.

Coherent photo-thermal noise cancellation in a dual-wavelength optical cavity for narrow-linewidth laser frequency stabilisation

Optical resonators are used for the realisation of ultra-stable frequency lasers. The use of high reflectivity multi-band coatings allows the frequency locking of several lasers of different wavelengths to a single cavity. While the noise processes for single wavelength cavities are well known, the correlation caused by multi-stack coatings has as yet not been analysed experimentally. In our work, we stabilise the frequency of a 729 nm and a 1069 nm laser to one mirror pair and determine the residual-amplitude modulation (RAM) and photo-thermal noise (PTN). We find correlations in PTN between the two lasers and observe coherent cancellation of PTN for the 1069 nm coating. We show that the fractional frequency instability of the 729 nm laser is limited by RAM at 1 × 10-14. The instability of the 1069 nm laser is at 3 × 10-15 close to the thermal noise limit of 1.5 × 10-15.

Cavity-Mediated Molecular Entanglement and Generation of Non-classical States of Light

The generation and control of entanglement in a quantum mechanical system are critical elements of nearly all quantum applications. Molecular systems are promising candidates, with numerous degrees of freedom able to be targeted. However, knowledge of intersystem entanglement mechanisms in such systems is limited. In this work, we demonstrate the generation of entanglement between vibrational degrees of freedom in molecules via strong coupling to a cavity mode driven by a weak coherent field. In a bimolecular system, we show that entanglement can be generated not only between the cavity and molecular system but also between molecules. This process also results in the generation of nonclassical states of light, providing potential pathways for harnessing entanglement in molecular systems.

Sympathetic Cooling and Slowing of Molecules with Rydberg Atoms

We propose to sympathetically slow and cool polar molecules in a cold, low-density beam using laser-cooled Rydberg atoms. The elastic collision cross sections between molecules and Rydberg atoms are large enough to efficiently thermalize the molecules even in a low-density environment. Molecules traveling at 100  m/s can be stopped in under 30 collisions with little inelastic loss. Our method does not require photon scattering from the molecules and can be generically applied to complex species for applications in precision measurement, quantum information science, and controlled chemistry.

Quantum-Enhanced Metrology for Molecular Symmetry Violation Using Decoherence-Free Subspaces

We propose a method to measure time-reversal symmetry violation in molecules that overcomes the standard quantum limit while leveraging decoherence-free subspaces to mitigate sensitivity to classical noise. The protocol does not require an external electric field, and the entangled states have no first-order sensitivity to static electromagnetic fields as they involve superpositions with zero average lab-frame projection of spins and dipoles. This protocol can be applied with trapped neutral or ionic species, and can be implemented using methods that have been demonstrated experimentally.

Trapping and Ground-State Cooling of a Single H_{2}^{+}

We demonstrate co-trapping and sideband cooling of a H_{2}^{+}-^{9}Be^{+} ion pair in a cryogenic Paul trap. We study the chemical lifetime of H_{2}^{+} and its dependence on the apparatus temperature, achieving lifetimes of up to 11_{-3}^{+6}  h at 10 K. We demonstrate cooling of two of the modes of translational motion to an average phonon number of 0.07(1) and 0.05(1), corresponding to a temperature of 22(1) and 55(3)  μK, respectively. Our results provide a basis for quantum logic spectroscopy experiments of H_{2}^{+}, as well as other light ions such as HD^{+}, H_{3}^{+}, and He^{+}.

Effects of an Oscillating Electric Field on and Dipole Moment Measurement of a Single Molecular Ion

We characterize and model the Stark effect due to the radio-frequency (rf) electric field experienced by a molecular ion in an rf Paul trap, a leading systematic in the uncertainty of the field-free rotational transition. The ion is deliberately displaced to sample different known rf electric fields and measure the resultant shifts in transition frequencies. With this method, we determine the permanent electric dipole moment of CaH^{+}, and find close agreement with theory. The characterization is performed by using a frequency comb which probes rotational transitions in the molecular ion. With improved coherence of the comb laser, a fractional statistical uncertainty for a transition line center of as low as 4.6×10^{-13} was achieved.

Resonant and non-resonant optimizations by multi-constraint quantum control theory in molecular rotational states

It is a promising research for optimization of quantum gate in the field of quantum computation. We investigate the feasibility of implementing the single-qubit gate (Hadamard) in molecular rotational system. By applying the Multi-constraint quantum optimal control method, the excepted final states can be achieved based on the molecular rotational states both in resonant and non-resonant cases with the control pulses. The permanent electric dipole moment is ignored in non-resonance. Besides, the zero-pulse area constraint and the constant fluence constraint are employed to optimize shapes of control pulses. Finally, we show that the Hadamard gate can be realized with the high fidelity (0.9999) and also examine the dependence of the fidelity on pulse fluence as well as the control pulse.

Atom Interferometer Driven by a Picosecond Frequency Comb

We demonstrate a light-pulse atom interferometer based on the diffraction of free-falling atoms by a picosecond frequency-comb laser. More specifically, we coherently split and recombine wave packets of cold ^{87}Rb atoms by driving stimulated Raman transitions between the |5s ^{2}S_{1/2},F=1⟩ and |5s ^{2}S_{1/2},F=2⟩ hyperfine states, using two trains of picosecond pulses in a counterpropagating geometry. We study the impact of the pulses' length as well as the interrogation time onto the contrast of the atom interferometer. Our experimental data are well reproduced by a numerical simulation based on an effective coupling that depends on the overlap between the pulses and the atomic cloud. These results pave the way for extending light-pulse interferometry to transitions in other spectral regions and therefore to other species, for new possibilities in metrology, sensing of gravito-inertial effects, and tests of fundamental physics.

Optimization two-qubit quantum gate by two optical control methods in molecular pendular states

Implementation of quantum gates are important for quantum computations in physical system made of polar molecules. We investigate the feasibility of implementing gates based on pendular states of the molecular system by two different quantum optical control methods. Firstly, the Multi-Target optimal control theory and the Multi-Constraint optimal control theory are described for optimizing control fields and accomplish the optimization of quantum gates. Numerical results show that the controlled NOT gate (CNOT) can be realized under the control of above methods with high fidelities (0.975 and 0.999) respectively. In addition, in order to examine the dependence of the fidelity on energy difference in the same molecular system, the SWAP gate in the molecular system is also optimized with high fidelity (0.999) by the Multi-Constraint optimal control theory with the zero-area and constant-fluence constraints.

Design and characterization of a cryogenic linear Paul ion trap for ion-neutral reaction studies

Ultra-high vacuum conditions are ideal for the study of trapped ions. They offer an almost perturbation-free environment, where ions confined in traps can be studied for extended periods of time-facilitating precision measurements and allowing infrequent events to be observed. However, if one wishes to study processes involving molecular ions, it is important to consider the effect of blackbody radiation (BBR). The vast majority of molecular ions interact with BBR. At 300 K, state selection in trapped molecular ions can be rapidly lost (in a matter of seconds). To address this issue, and to maintain state selectivity in trapped molecular ions, a cryogenic ion trap chamber has been constructed and characterized. At the center of the apparatus is a linear Paul ion trap, where Coulomb crystals can be formed for ion-neutral reaction studies. Optical access is provided, for lasers and for imaging of the crystals, alongside ion optics and a flight tube for recording time-of-flight mass spectra. The ion trap region, encased within two nested temperature stages, reaches temperatures below 9 K. To avoid vibrations from the cryocooler impeding laser cooling or imaging of the ions, vibration-damping elements are explicitly included. These components successfully inhibit the coupling of vibrations from the cold head to the ion trap-confirmed by accelerometer measurements and by the resolution of images recorded at the trap center (at 9 and 295 K). These results confirm that the cryogenic ion trap apparatus meets all requirements for studying ion-neutral reactions under cold, controlled conditions.

Ultra-low loss visible light waveguides for integrated atomic, molecular, and quantum photonics

Atomic, molecular and optical (AMO) visible light systems are the heart of precision applications including quantum, atomic clocks and precision metrology. As these systems scale in terms of number of lasers, wavelengths, and optical components, their reliability, space occupied, and power consumption will push the limits of using traditional laboratory-scale lasers and optics. Visible light photonic integration is critical to advancing AMO based sciences and applications, yet key performance aspects remain to be addressed, most notably waveguide losses and laser phase noise and stability. Additionally, a visible light integrated solution needs to be wafer-scale CMOS compatible and capable of supporting a wide array of photonic components. While the regime of ultra-low loss has been achieved at telecommunication wavelengths, progress at visible wavelengths has been limited. Here, we report the lowest waveguide losses and highest resonator Qs to date in the visible range, to the best of our knowledge. We report waveguide losses at wavelengths associated with strontium transitions in the 461 nm to 802 nm wavelength range, of 0.01 dB/cm to 0.09 dB/cm and associated intrinsic resonator Q of 60 Million to 9.5 Million, a decrease in loss by factors of 6x to 2x and increase in Q by factors of 10x to 1.5x over this visible wavelength range. Additionally, we measure an absorption limited loss and Q of 0.17 dB/m and 340 million at 674 nm. This level of performance is achieved in a wafer-scale foundry compatible Si₃N₄ platform with a 20 nm thick core and TEOS-PECVD deposited upper cladding oxide, and enables waveguides for different wavelengths to be fabricated on the same wafer with mask-only changes per wavelength. These results represent a significant step forward in waveguide platforms that operate in the visible, opening up a wide range of integrated applications that utilize atoms, ions and molecules including sensing, navigation, metrology and clocks.

High-Fidelity Bell-State Preparation with ^{40}Ca^{+} Optical Qubits

Entanglement generation in trapped-ion systems has relied thus far on two distinct but related geometric phase gate techniques: Mølmer-Sørensen and light-shift gates. We recently proposed a variant of the light-shift scheme where the qubit levels are separated by an optical frequency [B. C. Sawyer and K. R. Brown, Phys. Rev. A 103, 022427 (2021)PLRAAN2469-992610.1103/PhysRevA.103.022427]. Here we report an experimental demonstration of this entangling gate using a pair of ^{40}Ca^{+} ions in a cryogenic surface-electrode ion trap and a commercial, high-power, 532 nm Nd:YAG laser. Generating a Bell state in 35  μs, we directly measure an infidelity of 6(3)×10^{-4} without subtraction of experimental errors. The 532 nm gate laser wavelength suppresses intrinsic photon scattering error to ∼1×10^{-5}.

Engineering Long-Lived Vibrational States for an Organic Molecule

The optomechanical character of molecules was discovered by Raman about one century ago. Today, molecules are promising contenders for high-performance quantum optomechanical platforms because their small size and large energy-level separations make them intrinsically robust against thermal agitations. Moreover, the precision and throughput of chemical synthesis can ensure a viable route to quantum technological applications. The challenge, however, is that the coupling of molecular vibrations to environmental phonons limits their coherence to picosecond time scales. Here, we improve the optomechanical quality of a molecule by several orders of magnitude through phononic engineering of its surrounding. By dressing a molecule with long-lived high-frequency phonon modes of its nanoscopic environment, we achieve storage and retrieval of photons at millisecond timescales and allow for the emergence of single-photon strong coupling in optomechanics. Our strategy can be extended to the realization of molecular optomechanical networks.

From megahertz to terahertz qubits encoded in molecular ions: theoretical analysis of dipole-forbidden spectroscopic transitions in N2. Phys Chem Chem Phys 2020;22:23083-23098. [PMID: 33048077 DOI: 10.1039/d0cp03906c]

Recent advances in quantum technologies have enabled the precise control of single trapped molecules on the quantum level. Exploring the scope of these new technologies, we studied theoretically the implementation of qubits and clock transitions in the spin, rotational, and vibrational degrees of freedom of molecular nitrogen ions including the effects of magnetic fields. The relevant spectroscopic transitions span six orders of magnitude in frequency, illustrating the versatility of the molecular spectrum for encoding quantum information. We identified two types of magnetically insensitive qubits with very low ("stretched"-state qubits) or even zero ("magic" magnetic-field qubits) linear Zeeman shifts. The corresponding spectroscopic transitions are predicted to shift by as little as a few mHz for an amplitude of magnetic-field fluctuations on the order of a few mG, translating into Zeeman-limited coherence times of tens of minutes encoded in the rotations and vibrations of the molecule. We also found that the Q(0) line of the fundamental vibrational transition is magnetic-dipole allowed by interaction with the first excited electronic state of the molecule. The Q(0) transitions, which benefit from small systematic shifts for clock operation and is thus well suited for testing a possible variation in the proton-to-electron mass ratio, were so far not considered in single-photon spectra. Finally, we explored possibilities to coherently control the nuclear-spin configuration of N2+ through the magnetically enhanced mixing of nuclear-spin states.

Identification of molecular quantum states using phase-sensitive forces

Quantum-logic techniques used to manipulate quantum systems are now increasingly being applied to molecules. Previous experiments on single trapped diatomic species have enabled state detection with excellent fidelities and highly precise spectroscopic measurements. However, for complex molecules with a dense energy-level structure improved methods are necessary. Here, we demonstrate an enhanced quantum protocol for molecular state detection using state-dependent forces. Our approach is based on interfering a reference and a signal force applied to a single atomic and molecular ion. By changing the relative phase of the forces, we identify states embedded in a dense molecular energy-level structure and monitor state-to-state inelastic scattering processes. This method can also be used to exclude a large number of states in a single measurement when the initial state preparation is imperfect and information on the molecular properties is incomplete. While the present experiments focus on N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{2}^{+}$$\end{document}2+, the method is general and is expected to be of particular benefit for polyatomic systems.

The identification of molecular quantum states becomes challenging with increasing complexity of the molecular level structure. Here, the authors non-destructively identified excited molecular states of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\rm{N}}}_{2}^{+}$$\end{document}N2+ by interfering forces applied to both the molecular ion and to a co-trapped atomic ion.

Observation of Collisions between Two Ultracold Ground-State CaF Molecules

We measure inelastic collisions between ultracold CaF molecules by combining two optical tweezers, each containing a single molecule. We observe collisions between ^{2}Σ CaF molecules in the absolute ground state |X,v=0,N=0,F=0⟩, and in excited hyperfine and rotational states. In the absolute ground state, we find a two-body loss rate of 7(4)×10^{-11}  cm^{3}/s, which is below, but close to, the predicted universal loss rate.

Forming a Single Molecule by Magnetoassociation in an Optical Tweezer

We demonstrate the formation of a single NaCs molecule in an optical tweezer by magnetoassociation through an s-wave Feshbach resonance at 864.11(5) G. Starting from single atoms cooled to their motional ground states, we achieve conversion efficiencies of 47(1)%, and measure a molecular lifetime of 4.7(7) ms. By construction, the single molecules are predominantly [77(5)%] in the center-of-mass motional ground state of the tweezer. Furthermore, we produce a single p-wave molecule near 807 G by first preparing one of the atoms with one quantum of motional excitation. Our creation of a single weakly bound molecule in a designated internal state in the motional ground state of an optical tweezer is a crucial step towards coherent control of single molecules in optical tweezer arrays.