Rotational states of ultracold polar molecules possess long lifetimes, microwave-domain coupling, and tunable dipolar interactions. The availability of numerous rotational states has inspired many applications, including simulating quantum magnetism, encoding high-dimensional qudits and generating large synthetic dimensions. However, engineering the coherent superpositions of multiple rotational states needed for these applications is difficult owing to strong differential light shifts. Here, we overcome this challenge using individual molecules confined in near-magic wavelength optical tweezers. Through precision Ramsey spectroscopy, we find the exact magic wavelengths and sensitivities to detuning errors for multiple rotational state superpositions. We find for traps polarised parallel to the quantisation axis, the magic wavelengths are closely clustered enabling long-lived coherence across multiple rotational states simultaneously. Using a generalised Ramsey sequence, we demonstrate second-scale coherent spin-1 dynamics encoded in three rotational states and perform multiparameter estimation. With modest experimental improvements, we predict second-scale coherence across ten rotational states is achievable.
Rotational states of ultracold polar molecules possess long lifetimes, microwave-domain coupling, and tunable dipolar interactions. The availability of numerous rotational states has inspired many applications, including simulating quantum magnetism, encoding high-dimensional qudits and generating large synthetic dimensions. However, engineering the coherent superpositions of multiple rotational states needed for these applications is difficult owing to strong differential light shifts. Here, we overcome this challenge using individual molecules confined in near-magic wavelength optical tweezers. Through precision Ramsey spectroscopy, we find the exact magic wavelengths and sensitivities to detuning errors for multiple rotational state superpositions. We find for traps polarised parallel to the quantisation axis, the magic wavelengths are closely clustered enabling long-lived coherence across multiple rotational states simultaneously. Using a generalised Ramsey sequence, we demonstrate second-scale coherent spin-1 dynamics encoded in three rotational states and perform multiparameter estimation. With modest experimental improvements, we predict second-scale coherence across ten rotational states is achievable.
Abstract Ultracold polar molecules combine a rich structure of long-lived internal states with access to controllable long-range anisotropic dipole–dipole interactions. In particular, the rotational states of polar molecules confined in optical tweezers or optical lattices may be used to encode interacting qubits for quantum computation or pseudo-spins for simulating quantum magnetism. As with all quantum platforms, the engineering of robust coherent superpositions of states is vital. However, for optically trapped molecules, the coherence time between rotational states is typically limited by inhomogeneous differential light shifts. Here we demonstrate a rotationally magic optical trap for 87 Rb 133 Cs molecules that supports a Ramsey coherence time of 0.78(4) s in the absence of dipole–dipole interactions. This is estimated to extend to >1.4 s at the 95% confidence level using a single spin-echo pulse. In our trap, dipolar interactions become the dominant mechanism by which Ramsey contrast is lost for superpositions that generate oscillating dipoles. By changing the states forming the superposition, we tune the effective dipole moment and show that the coherence time is inversely proportional to the strength of the dipolar interaction. Our work unlocks the full potential of the rotational degree of freedom in molecules for quantum computation and quantum simulation.
Abstract Realizing quantum control and entanglement of particles is crucial for advancing both quantum technologies and fundamental science. Substantial developments in this domain have been achieved in a variety of systems 1–5 . In this context, ultracold polar molecules offer new and unique opportunities because of their more complex internal structure associated with vibration and rotation, coupled with the existence of long-range interactions 6,7 . However, the same properties make molecules highly sensitive to their environment 8–10 , affecting their coherence and utility in some applications. Here we show that by engineering an exceptionally controlled environment using rotationally magic 11,12 optical tweezers, we can achieve long-lived entanglement between pairs of molecules using detectable hertz-scale interactions. We prepare two-molecule Bell states with fidelity 0.924−0.016+0.013 0.92 4 − 0.016 + 0.013 , limited by detectable leakage errors. When correcting for these errors, the fidelity is 0.976−0.016+0.014 0.97 6 − 0.016 + 0.014 . We show that the second-scale entanglement lifetimes are limited solely by these errors, providing opportunities for research in quantum-enhanced metrology 7,13 , ultracold chemistry 14 and the use of rotational states in quantum simulation, quantum computation and as quantum memories. The extension of precise quantum control to complex molecular systems will enable their additional degrees of freedom to be exploited across many domains of quantum science 15–17 .
Ultracold polar molecules have become the subject of burgeoning fields of research in recent years owing to their prospects in quantum simulation, quantum computation and precision measurement. Their relatively large ground state dipole moment, coupled with a complex internal structure forms an incredibly powerful toolbox in which to perform quantum science experiments. Unfortunately, spatial confinement using light, which is necessary for many of the aforementioned applications, causes differential ac Stark shifts between quantum states, limiting coherence times and stifling their applicability. By accessing a so-called magic condition, this effect can be eliminated. This thesis presents work towards producing a quantum simulator based on a bulk gas of 87Rb133Cs molecules. We develop a magic wavelength trap by exploring nominally forbidden transitions from the X1Σ + ground state to b 3Π0 states. By tuning our trapping laser between transitions to different vibrational states of b3Π0, we can arbitrarily tune the difference in polarisability between pairs of rotational states and engineer second-scale coherence times. When we trap our molecules in a superposition of rotational states that exhibit a dipole moment in the laboratory frame, we observe the effects of long-range dipole-dipole interactions between molecules. These dipole-dipole interactions form the basis for quantum simulation and computation applications, observations of which marks an important milestone for realising a quantum simulator using 87Rb133Cs. We then demonstrate a route to ground state 87Rb133Cs molecules that is compatible with a protocol for loading Feshbach molecules into an optical lattice, developed by researchers at the University of Innsbruck. This method can be combined with a magic wavelength trap to produce a sample of 87Rb133Cs molecules in a magic lattice. Finally, we engineer synthetic dimensions that simulate simple single-particle Hamiltonians by coupling multiple rotational states in 87Rb133Cs. This forms the foundations for utilising rotational states of diatomic molecules as a platform for exploring synthetic dimensions
Abstract Quantum states with long-lived coherence are essential for quantum computation, simulation and metrology. The nuclear spin states of ultracold molecules prepared in the singlet rovibrational ground state are an excellent candidate for encoding and storing quantum information. However, it is important to understand all sources of decoherence for these qubits, and then eliminate them, in order to reach the longest possible coherence times. Here, we fully characterise the dominant mechanisms for decoherence of a storage qubit in an optically trapped ultracold gas of RbCs molecules using high-resolution Ramsey spectroscopy. Guided by a detailed understanding of the hyperfine structure of the molecule, we tune the magnetic field to where a pair of hyperfine states have the same magnetic moment. These states form a qubit, which is insensitive to variations in magnetic field. Our experiments reveal an unexpected differential tensor light shift between the states, caused by weak mixing of rotational states. We demonstrate how this light shift can be eliminated by setting the angle between the linearly polarised trap light and the applied magnetic field to a magic angle of arccos(1/√3)≈55°. This leads to a coherence time exceeding 6.9 s (90% confidence level). Our results unlock the potential of ultracold molecules as a platform for quantum computation.
This thesis presents the development of a toolbox for the coherent control of ultracold polar molecules. Such systems of molecules promise the creation of long-lived, highly dipolar quantum gases with applications spanning the fields of quantum state controlled chemistry, quantum information, quantum simulation, and precision measurement. However, the addition of vibrational and rotational degrees of freedom leads to molecular systems being significantly more complex than their widely used atomic counterparts. In this work we demonstrate full control of the quantum state down to the hyperfine level of an optically trapped sample of ultracold bosonic 87Rb133 Cs molecules, and exploit that control to begin an investigation into the collision processes which take place in an ultracold molecular gas. We create a sample of up to ∼ 4000 optically trapped molecules in their rovibronic and hyperfine ground state. We characterise the molecules by measuring their temperature, binding energy, and molecule-frame electric dipole moment. We perform spectroscopy of the first rotationally excited state with hyperfine state resolution using microwaves to determine accurate values of rotational and hyperfine coupling constants. We use coherent π pulses to perform complete transfer population between selected hyperfine levels of the ground, first-excited, and second-excited rotational states. We investigate the effect of the off-resonant light of our optical dipole trap on the rotational and hyperfine structure of the molecules. Through a combination of high-resolution microwave spectroscopy and parametric heating measurements, we characterise the polarisability of the 87Rb133Cs molecule. We demonstrate that coupling between neighbouring hyperfine states manifests in rich structure with many avoided crossings in any rotational state other than the ground state. This coupling may be tuned by rotating the polarisation of the linearly polarised trapping light. Finally, we study the lifetime of polar bosonic 87Rb133Cs molecules in our 3D optical dipole trap. We examine the lifetime of the molecules as a function of dipole trap intensity, magnetic field, and hyperfine and rotational state. Despite the chemical stability of the 87Rb133 Cs molecule, we observe lifetimes of ∼1 s corresponding to 2-body decay rates close to the universal limit.
Abstract Molecules have vibrational, rotational, spin-orbit and hyperfine degrees of freedom or quantum states, each of which responds in a unique fashion to external electromagnetic radiation. The control over superpositions of these quantum states is key to coherent manipulation of molecules. For example, the better the coherence time the longer quantum simulations can last. The important quantity for controlling an ultracold molecule with laser light is its complex-valued molecular dynamic polarizability. Its real part determines the tweezer or trapping potential as felt by the molecule, while its imaginary part limits the coherence time. Here, our study shows that efficient trapping of a molecule in its vibrational ground state can be achieved by selecting a laser frequency with a detuning on the order of tens of GHz relative to an electric-dipole-forbidden molecular transition. Close proximity to this nearly forbidden transition allows to create a sufficiently deep trapping potential for multiple rotational states without sacrificing coherence times among these states from Raman and Rayleigh scattering. In fact, we demonstrate that magic trapping conditions for multiple rotational states of the ultracold 23Na87Rb polar molecule can be created.