We explore the total cross section of ground state polar molecules in an electric field at various energies, focusing on RbCs and RbK. An external electric field polarizes the molecules and induces strong dipolar interactions leading to non-zero partial waves contributing to the scattering even as the collision energy goes to zero. This results in the need to compute scattering problems with many different values of total M to converge the total cross section. An accurate and efficient approximate total cross section is introduced and used to study the low field temperature dependence. To understand the scattering of the polar molecules we compare a semi-classical cross section with quantum unitarity limit. This comparison leads to the ability to characterize the scattering based on the value of the electric field and the collision energy.
A detailed treatment of an electro-optical trap for polar molecules, realized by embedding an optical trap within a uniform electrostatic field, is presented and the trap's properties analyzed and discussed. The electro-optical trap offers significant advantages over an optical trap that include an increased trap depth and conversion of alignment of the trapped molecules to marked orientation. Tilting the polarization plane of the optical field with respect to the electrostatic field diminishes both the trap depth and orientation and lifts the degeneracy of the $\pm M$ states of the trapped mo…
We study the ionization dynamics of oriented HeH$^+$ in strong linearly-polarized laser fields by numerically solving the time-dependent Schrödinger equation. The calculated photoelectron momentum distributions for parallel orientation show a striking asymmetric structure. With a developed model pertinent to polar molecules, we trace the electron motion in real time. We show that this asymmetric structure arises from the interplay of the Coulomb effect and the permanent dipole in strong laser fields. This structure can be used to probe the degree of orientation which is important in ultrafast …
External field control of spin-dependent rotational decoherence of ultracold polar molecules
我们确定超冷极性分子的捕获条件，其中对内部状态经历相同的捕获电位。这样的条件可以确保显著降低超冷样品中不可避免的不均匀性的有害影响。特别是，我们调查的内部旋转和超精细量子态的超冷费米子基态$^{40}$ K $^{87}$ Rb极性分子，当静磁场，静电场，和陷阱激光场同时施加。理解改变这三个场的相对取向或偏振的效果对于从两个或更多个旋转振动态构建无退相干子空间至关重要。此外，我们评估在这些领域的存在下，这将允许控制分子之间的相互作用在不同的网站的光晶格和研究的相互作用各向异性的影响的能力，纠缠极性分子的诱导偶极矩的分子。
We demonstrate loading of SrF molecules into an optical dipole trap (ODT) via in-trap $Λ$-cooling. We find that this cooling can be optimized by a proper choice of relative ODT and $Λ$ beam polarizations. In this optimized configuration, we observe molecules with temperatures as low as 14(1) $μ$K in traps with depths up to 570 $μ$K. With optimized parameters, we transfer $\!\sim\!5$% of molecules from our radio-frequency magneto-optical trap into the ODT, at a density of $\sim\!2\times 10^{9}$ cm$^{-3}$, a phase space density of $\sim\!2\times 10^{-7}$, and with a trap lifetime of $\!\sim\!1$ …
Ultralong-range polyatomic Rydberg molecules formed by a polar perturber
里德伯原子电子的内部电场可以束缚极性分子，形成一个巨大的超远程稳定的多原子分子。这些分子不仅与里德伯原子共享它们的性质，它们还具有巨大的永久电偶极矩，并且还允许极性分子取向的相干控制。在这项工作中，我们包括额外的里德伯流形耦合到近简并的里德伯态[S。T. Rittenhouse和H. R. Sadeghpour，Phys. Rev. Lett. 104，243002（2010）]。一组$(n+3)s$ Rydberg态与碱金属原子中的$n(l>2)$近简并Rydberg流形的耦合导致Born-Oppenheimer势中明显的避免交叉。最终，这些避免的交叉使标准的双光子激光光缔合技术的巨型多原子里德堡分子的形成。
Because molecules can have their orientation locked when embedded into a solid rare-gas matrix, their hyperfine structure is strongly perturbed relative to the freely rotating molecule. The addition of an electric field further perturbs the structure, and fields parallel and antiparallel to the molecular orientation result in different shifts of the hyperfine structure. These shifts enable the selective detection of molecules with different orientations relative to the axes of a rare-gas crystal, which will be an important ingredient of an improved electron electric dipole moment measurement u…
State-dependent optical tweezers can be used to trap a pair of molecules with a separation much smaller than the wavelength of the trapping light, greatly enhancing the dipole-dipole interaction between them. Here we describe a general approach to producing these state-dependent potentials using the tensor part of the ac Stark shift and show how it can be used to carry out two-qubit gates between pairs of molecules. The method is applicable to broad classes of molecules including bialkali molecules produced by atom association and those amenable to direct laser cooling.
We proposed a general Zeeman slower scheme applicable to the majority of the laser-coolable molecules. Different from previous schemes, the key idea of our scheme lies in that the compensation of the detuning with the magnetic field is done for the repumping laser instead of the cooling laser. Only atoms or molecules with the right velocity will be repumped and laser slowed. Such scheme is more feasible for molecules with complex energy sturcutres. We apply this scheme for molecules with large Landé g-factor of the excited states and polyatomic molecules, and it shows a better slowing efficien…
We explore the electronic structure of ultralong-range pentaatomic Rydberg molecules from a merger of a Rydberg atom and two ground state heteronuclear diatomic molecules. Our focus is on the interaction of Rb($23s$) and Rb($n=20$, $l\ge 3$) Rydberg states with ground and rotationally excited KRb diatomic polar molecules. For symmetric and asymmetric configurations of the pentaatomic Rydberg molecule, we investigate the metamorphosis of the Born-Oppenheimer potential curves, essential for the binding of the molecule, with varying distance from the Rydberg core and analyze the alignment and ori…
A model for positron binding to polar molecules is considered by combining the dipole potential outside the molecule with a strongly repulsive core of a given radius. Using existing experimental data on binding energies leads to unphysically small core radii for all of the molecules studied. This suggests that electron-positron correlations neglected in the simple model play a large role in determining the binding energy. We account for these by including polarization potential via perturbation theory and non-perturbatively. The perturbative model makes reliable predictions of binding energies…
We analyze in detail the possibility to use charge-dipole interaction between a single polar molecule or a 1D molecular array and a single Rydberg atom to read out rotational populations. The change in the Rydberg electron energy is conditioned on the rotational state of the polar molecules, allowing for realization of a CNOT quantum gate between the molecules and the atom. Subsequent readout of the atomic fluorescence results in a non-destructive measurement of the rotational state. We study the interaction between a 1D array of polar molecules and an array or a cloud of atoms in a Rydberg su…
Fully internal and motional state controlled and individually manipulable polar molecules are desirable for many quantum science applications leveraging the rich state space and intrinsic interactions of molecules. While prior efforts at assembling molecules from their constituent atoms individually trapped in optical tweezers achieved such a goal for exactly one molecule, here we extend the technique to an array of five molecules, unlocking the ability to study molecular interactions. We detail the technical challenges and solutions inherent in scaling this system up. With parallel preparatio…
A highly sensitive, general, and preferably nondestructive technique to detect polar molecules would greatly advance a number of fields, in particular quantum science with cold and ultracold molecules. Here, we propose using resonant energy transfer between molecules and Rydberg atoms to detect molecules. Based on an energy transfer cross section of $>10^{-6}\,$cm$^2$ for sufficiently low collision energies, a near unit efficiency non-destructive detection of basically any polar molecule species in a well defined internal state should be possible.
It has long been expected that quantum degenerate gases of molecules would open access to a wide range of phenomena in molecular and quantum sciences. However, the very complexity that makes ultracold molecules so enticing has made reaching degeneracy an outstanding experimental challenge over the past decade. We now report the production of a Fermi degenerate gas of ultracold polar molecules of potassium--rubidium (KRb). Through coherent adiabatic association in a deeply degenerate mixture of a rubidium Bose-Einstein condensate and a potassium Fermi gas, we produce molecules at temperatures b…
We investigate the use of microwave radiation to produce a repulsive shield between pairs of ultracold polar molecules and prevent collisional losses that occur when molecular pairs reach short range. We carry out coupled-channels calculations on RbCs+RbCs and CaF+CaF collisions in microwave fields. We show that effective shielding requires predominantly circular polarization, but can still be achieved with elliptical polarization that is around 90% circular.
Qubit coherence times are critical to the performance of any robust quantum computing platform. For quantum information processing using arrays of polar molecules, a key performance parameter is the molecular rotational coherence time. We report a 93(7) ms coherence time for rotational state qubits of laser cooled CaF molecules in optical tweezer traps, over an order of magnitude longer than previous systems. Inhomogeneous broadening due to the differential polarizability between the qubit states is suppressed by tuning the tweezer polarization and applied magnetic field to a "magic" angle. Th…
Strong-field ionization of polar molecules contains rich dynamical processes such as tunneling, excitation, and Stark shift. These processes occur on a sub-cycle time scale and are difficult to distinguish in ultrafast measurements. Here, with a developed strong-field model considering effects of both Coulomb and permanent dipole, we show that photoelectron momentum distributions (PMDs) in orthogonal two-color laser fields can be utilized to resolve these processes with attosecond-scale resolution. A feature quantity related to the asymmetry in PMDs is obtained, with which the complex electron…
We report measurements of the ac polarizabilities of ultracold ground-state $^{23}\rm{Na}^{87}\rm{Rb}$ molecules. While the polarizability of the ground rotational state $J = 0$ is isotropic, that of the first excited rotational state $J = 1$ is anisotropic and depends strongly on the light polarization angle. We obtain both polarizabilities precisely by combining trap oscillation frequency measurement and high resolution rotational spectroscopy driven by microwave. With the optimized light polarization angle and intensity combination, the nonuniformity of the differential ac Stark shift betwe…
We analyze the electric dipole moments (PDMs) and static electric dipole polarizabilities of the alkali--alkaline-earth (Alk-AlkE) dimers by employing finite-field coupled-cluster methods, both in the frameworks of non-relativistic and four-component spinfree relativistic theory. In order to carry out comparative analyses rigorously, we consider those Alk-AlkE molecules made out of the lightest to the medium-heavy constituent atoms (Alk: Li to Rb and AlkE: Be through Sr). We present behaviour of electron correlation effects as well as relativistic effects with the size of the molecules. Uncert…
Vibrational spectroscopy of polar molecules with superradiance
本文研究了在高光学深度（OD）样品中极性分子光谱中振动跃迁的合作现象和超辐射。这种协同性来自于通过偶极-偶极相互作用建立的粒子间相干性，并导致衰变过程的加速。我们将我们的计算与最近的工作进行比较[Deiglmayr等人，EUR. J. D 65，99（2011）]，并且发现非常好的一致性，这表明超辐射效应需要包括在各种各样的超冷分子设置中，包括振动和旋转状态。
We propose a very sensitive method for measuring the electric dipole moment of the electron using polar molecules embedded in a cryogenic solid matrix of inert-gas atoms. The polar molecules can be oriented in the $\hat{\rm{z}}$ direction by an applied electric field, as has recently been demonstrated by Park, et al. [Angewandte Chemie {\bf 129}, 1066 (2017)]. The trapped molecules are prepared into a state which has its electron spin perpendicular to $\hat{\rm{z}}$, and a magnetic field along $\hat{\rm{z}}$ causes precession of this spin. An electron electric dipole moment $d_e$ would affect …
We report the creation of ultracold bosonic dipolar $^{23}\textrm{Na}^{39}\textrm{K}$ molecules in their absolute rovibrational ground state. Starting from weakly bound molecules immersed in an ultracold atomic mixture, we coherently transfer the dimers to the rovibrational ground state using an adiabatic Raman passage. We analyze the two-body decay in a pure molecular sample and in molecule-atom mixtures and find an unexpectedly low two-body decay coefficient for collisions between molecules and $^{39}\textrm{K}$ atoms in a selected hyperfine state. The preparation of bosonic $^{23}\textrm{Na…
This paper reviews recent advances in the study of strongly interacting systems of dipolar molecules. Heteronuclear molecules feature large and tunable electric dipole moments, which give rise to long-range and anisotropic dipole-dipole interactions. Ultracold samples of dipolar molecules with long-range interactions offer a unique platform for quantum simulations and the study of correlated many-body physics. We provide an introduction to the physics of dipolar quantum gases, both electric and magnetic, and summarize the multipronged efforts to bring dipolar molecules into the quantum regime.…
We investigate the effect of far-off-resonant trapping light on ultracold bosonic RbCs molecules. We use kHz-precision microwave spectroscopy to measure the differential AC Stark shifts between the ground and first excited rotational levels of the molecule with hyperfine-state resolution. We demonstrate through both experiment and theory that coupling between neighboring hyperfine states manifests in rich structure with many avoided crossings. This coupling may be tuned by rotating the polarization of the linearly polarized trapping light. A combination of spectroscopic and parametric heating …
We demonstrate the coherent creation of a single NaCs molecule in its rotational, vibrational, and electronic (rovibronic) ground state in an optical tweezer. Starting with a weakly bound Feshbach molecule, we locate a two-photon transition via the $|{c^3Σ,v'=26}\rangle$ excited state and drive coherent Rabi oscillations between the Feshbach state and a single hyperfine level of the NaCs rovibronic ground state $|{X^1Σ,v''=0,N''=0}\rangle$ with a binding energy of $D_0 = h \times 147038.30(2)$ GHz. We measure a lifetime of $3.4\pm1.6$ s for the rovibronic ground-state molecule, which possesses…
Superpositions of rotational states in polar molecules induce strong, long-range dipolar interactions. Here we extend the rotational coherence by nearly one order of magnitude to 8.7(6) ms in a dilute gas of polar $^{23}$Na$^{40}$K molecules in an optical trap. We demonstrate spin-decoupled magic trapping, which cancels first-order and reduces second-order differential light shifts. The latter is achieved with a dc electric field that decouples nuclear spin, rotation and trapping light field. We observe density-dependent coherence times, which can be explained by dipolar interactions in the bu…
Electron rescattering and the fragmentation dynamics of molecules in strong optical fields
我们已经探讨了在一个弯曲的三原子分子，水，非平面分子，甲醇，和一个平面的环状结构的分子，苯，使用100 fs的线性和圆偏振，红外，强度选择的激光脉冲的碎裂动力学。在大于10 $^{15}$ W cm $^{-2}$的激光强度下，当光被圆偏振时，来自这些分子的单电荷和多电荷原子碎片的产率被抑制。在较低的强度下，碎片离子产率不是显著的极化依赖性。这种迄今未观察到的强度依赖于光的偏振态上的碎裂动力学的效果是合理的，使用一个简单的电子再散射模型。圆极化开关“关闭”电子再散射，并导致抑制多重电离和分子碎片。此外，抑制的程度取决于从光场到分子的能量转移的量：特定碎裂通道所需的能量转移越大，当使用圆偏振时其抑制越显著。
We use microwaves to engineer repulsive long-range interactions between ultracold polar molecules. The resulting shielding suppresses various loss mechanisms and provides large elastic cross sections. Hyperfine interactions limit the shielding under realistic conditions, but a magnetic field allows suppression of the losses to below 10-14 cm3 s-1. The mechanism and optimum conditions for shielding differ substantially from those proposed by Gorshkov et al. [Phys. Rev. Lett. 101, 073201 (2008)], and do not require cancelation of the long-range dipole-dipole interaction that is vital to many app…
We study polar molecule scattering in quasi-one-dimensional geometries. Elastic and reactive collision rates are computed as a function of collision energy and electric dipole moment for different confinement strengths. The numerical results are interpreted in terms of first order scattering and of adiabatic models. Universal dipolar scattering is also discussed. Our results are relevant to experiments where control of the collision dynamics through one dimensional confinement and an applied electric field is envisioned.
We measure inelastic collisions between ultracold CaF molecules by combining two optical tweezers, each containing a single molecule. We observe collisions between $^2Σ$ CaF molecules in the absolute ground state $|X,v=0, N=0,F=0\rangle$, and in excited hyperfine and rotational states. In the absolute ground state, we find a two-body loss rate of $7(4) \times 10^{-11} \text{cm}^{3}/\text{s}$, which is below, but close to the predicted universal loss rate.
We spectroscopically investigate a pathway for the conversion of $^{23}\textrm{Na}^{39}\textrm{K}$ Feshbach molecules into rovibronic ground state molecules via STImulated Raman Adiabatic Passage (STIRAP). Using photoassociation spectroscopy from the diatomic scattering threshold in the $a^3Σ^+$ potential, we locate the resonantly mixed electronically excited intermediate states $|B^1Π, v=8\rangle$ and $|c^3Σ^+, v=30\rangle$ which, due to their singlet-triplet admixture, serve as an ideal bridge between predominantly $a^3Σ^+$ Feshbach molecules and pure $X^1Σ^+$ ground state molecules. We inve…
