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arXiv:2609.33475

How many photons can a molecule scatter before its coherence is lost?

M. R. Tarbutt

quant-phphysics.atom-phSubmitted Sep 27, 2026• Announced Sep 29, 2026• 0 citations
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Abstract

Molecular qubits held in conservative optical traps may lose coherence when they scatter photons from the trapping lasers. The rate for this process has two parts, one equal to the mean Raman scattering rate of the two qubit states, and the other proportional to the square of the difference in their Rayleigh scattering amplitudes. This paper calculates the decoherence rate, expressing results in terms of the vector and tensor parts of the molecular polarizability, $α_1$ and $α_2$. While the decoherence rate is generally much larger for molecules than for atoms, it is suppressed at wavelengths where $α_1$ and $α_2$ are both small. The wavelengths where this occurs are identified for CaF molecules.

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We study a novel property of light scattering by Rb atoms confined in a far off-resonance optical dipole force trap. The trapping laser wavelength varies from 780 nm to 860 nm and its intensity is about 1 MW/cm{sup 2}. Spontaneous Raman scattering of photons from the trapping laser can change the ground-state hyperfine quantum number F of the atoms. We observe the relaxation time by measuring the population of the F=3 level after optically pumping the atoms into the F=2 level. Spontaneous photon scatter rates as low as 10{sup 3} s{sup -1} have been observed, corresponding to recoil heating rates below 1 mK/s. For detuning from resonance {Delta} greater than the excited-state fine-structure splitting the total scatter rate, including Rayleigh scattering, decreases as {Delta}{sup 2} while the spontaneous Raman scatter rate decreases as {Delta}{sup 4}. This is due to interference between the Raman scattering amplitudes from the two excited-state fine-structure levels in the Kramers-Heisenberg formula. Because Rayleigh scattering dominates, the atoms` F and M{sub F} quantum numbers are preserved even after many scattering events. This makes far off-resonance optical traps ideal for studies of state-selective collisions and collective phenomena.
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. The coherence time is limited by the residual differential polarizability, implying improvement with further cooling. A single spin-echo pulse is able to extend the coherence time to nearly half a second. The measured coherence times demonstrate the potential of polar molecules as high fidelity qubits.
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.
From studies of fundamental physics to quantum technologies the production of ultracold molecules will have a huge impact across a range of applications. For many years laser cooling, which became an invaluable tool in cold atomic physics, was deemed to be too impractical for application to molecules. Nevertheless, laser cooling has now been demonstrated for a few molecular species. Using a frequency-chirped laser slowing technique, the velocity distribution of a pulse of CaF molecules is compressed and slowed from 180 m/s to about 10 m/s. These slow molecules are then captured in a magneto-optical trap. I present measurements that show how the number of molecules, the photon scattering rate, the oscillation frequency, damping constant, temperature, cloud size and lifetime depend on the key parameters of the magneto-optical trap, especially the intensity and detuning of the main cooling laser. The trap contains up to 2*10^4 molecules, the maximum photon scattering rate is 2.5*10^6 s-1 per molecule, the maximum oscillation frequency is 100 Hz, the maximum damping constant is 500 s^-1, and the minimum rms radius of the trapped cloud is 1.5 mm. A minimum temperature of 730 microkelvin is obtained by ramping down the laser intensity to lower values. To reach lower temperatures, the cloud is loaded into a blue-detuned optical molasses, which cools the molecules to 55 microkelvin, well below the Doppler-limiting temperature. I characterise the cooling process and suggest the sub-Doppler mechanisms responsible. These ultracold molecules are the optically pumped into a single quantum state, and coherently transferred between selected hyperfine components of the ground and first-excited rotational states. Finally, the ultracold, state-selected molecules are loaded into a magnetic trap that has a lifetime of about 1 s.
Light scattering by isolated small and intermediate-size molecules is studied theoretically. A quantum-mechanical model is developed that treats the molecule and the radiation field on equal terms and allows a nonperturbative solution for arbitrary wave forms and field strengths. The molecular states are described in terms of a basis set of zeroth-order states chosen so as to minimize the number of excited molecular states in the laser frequency range that combines radiatively with the initial (ground) state, i.e., that act as doorways for the field. Detailed calculations are restricted to the case of a single doorway. Closed-form expressions are obtained for the frequency-resolved scattering rates and time-resolved scattering spectra, including fluorescence and Rayleigh–Raman components, for a variety of conditions, including δ(t) excitation, excitation by a Lorentzian light pulse, by a coherent train of pulses and stationary excitation. The case of nonlinear scattering by very intense pulses is also investigated. Model calculations are reported for systems of 1–3 molecular levels. It is found that in general phase relations are maintained so that the coherence survives as long as the signal.
We provide an expression for the decoherence rate in spatial superpositions due to scattering or collision with air molecules which is independent of the wavelength of the air molecules. This result reproduces the short- and long-wavelength limits known in the literature. We compare the decoherence rate with several existing interpolations in the literature and evaluate the decoherence rate and experimental parameters when creating macroscopic quantum spatial superpositions (i.e., in micron-size spheres). The interpolation regime is relevant in, e.g., matter-wave interferometry, where one might switch between the wavelength limits during the experimental protocol. Finally, we consider the decoherence rate's time dependence while creating and closing the spatial superposition in an interferometer setup.