Spin Interferometer with Ultracold YbF Molecules

• The paper demonstrates a novel spin interferometer using ultracold YbF molecules to achieve precise electron EDM measurements with enhanced statistical sensitivity.
• It details an advanced cooling and state preparation methodology that increases ultracold molecule brightness and reduces systematic errors.
• The study extends the technique to multilevel spin interferometry and ‘magic’ trapping, paving the way for second-scale coherence and multiparameter precision.

A spin interferometer using ultracold YbF molecules is an apparatus that exploits coherent superpositions of molecular hyperfine or rotational states for precision measurement, notably the search for the electron electric dipole moment (eEDM). The system leverages advanced molecular beam cooling, quantum state control, and high-efficiency detection to provide improved statistical sensitivity and robustness to systematic errors compared to previous molecular beam techniques. This platform also enables generalizable multilevel spin interferometry, encompassing both two-state (spin-1/2) and three-state (spin-1) interferometers, and operates in a regime of long coherence times facilitated by “magic” trapping conditions and sub-millikelvin temperatures.

1. Generation of the Ultracold YbF Molecular Beam

YbF molecules are generated in a cryogenic buffer-gas beam source. Ablation of a Yb rod inside a 3.7 K helium cell (He flow 1 sccm, ablation energy 40 mJ, 5 Hz repetition rate) yields pulses with mean forward velocity $v_0 \approx 170\,\mathrm{m/s}$ and millimeter-scale transverse extent (Jenkins et al., 31 Jan 2026). Immediately downstream, a two-dimensional optical molasses implements magnetically assisted Sisyphus cooling over 0.20 m (centered 0.70 m from the source). The main cooling transition is $$X^2\Sigma^+(v=0,N=1) \rightarrow A^2\Pi_{1/2}(v=0,J=1/2)$$ at 552 nm, detuned $+34$ MHz from the $F=1^-$ manifold, with repumpers at 568 nm ($v=1$) and 565 nm ($v=2$), all carrying rf sidebands for hyperfine closure (Alauze et al., 2021). A bias magnetic field of $\sim100\,\mu\mathrm{T}$ at 45° to the polarization disrupts dark states and enables sub-Doppler cooling.

After molasses, the transverse temperature is reduced to $T_\perp\approx 100\,\mu\mathrm{K}$ for both $x$ and $z$, increasing the flux of molecules with $v<150\,\mathrm{m/s}$ by over an order of magnitude and yielding a phase-space density $O(10^{-12})$. The ultracold beam exhibits a transverse velocity spread $\Delta v_\perp \sim 0.1\,\mathrm{m/s}$, with over $2 \times 10^5$ ultracold molecules per shot detected 1.5 m downstream—a 300-fold improvement in brightness compared to the uncooled beam (Alauze et al., 2021).

2. Quantum-State Preparation and Interferometer Basis

Molecules are initially in the ground state manifold $X^2\Sigma^+(v=0,N=1)$ after cooling. Quantum-state preparation is achieved via optical pumping and microwave transfer into $N=0$. The relevant hyperfine states are:

• $|0\rangle$: $F=0,\,m_F=0$
• $|F=1,\,m_F=\pm1\rangle$: these states, and their symmetric ($|x\rangle$) and antisymmetric ($|y\rangle$) combinations, define the interferometer “arms.”

Optical pumping from $N=1$ to $N=0$ (“dark” state $|0\rangle$) utilizes two 29 GHz microwave tones ($N=1\rightarrow2$) and laser cycles from $N=2$ and $N=0,1$ to $A^-$, leading to a measured optical pumping efficiency $\epsilon_\mathrm{OP} = 0.738(11)$ (Jenkins et al., 31 Jan 2026). Residual population in $N=1$ is quantified as $P_\mathrm{bg}=2.33(4)\%$.

The basis for the effective two-level interferometer is given by $$|y\rangle = i(|F=1,m_F=+1\rangle - |F=1,m_F=-1\rangle)/\sqrt{2}$$ and $$|x\rangle = (|F=1,m_F=+1\rangle + |F=1,m_F=-1\rangle)/\sqrt{2}$$.

3. Beam-Splitter and Recombiner: Stimulated Raman Interactions

The spin interferometry sequence is realized using spatially separated Raman beam pairs acting as beam-splitters and recombiners (Jenkins et al., 31 Jan 2026). Two co-propagating laser beams (polarization $z$ and $y$) address $|0\rangle \leftrightarrow |e^-\rangle$ and $|F=1, m_F=\pm1\rangle \leftrightarrow |e^-\rangle$ transitions, respectively. The system is described by an effective two-level Hamiltonian in the $\{|0\rangle,|y\rangle\}$ subspace: $$H = \frac{\hbar}{2}\left( \Omega_\text{eff} \sigma_x + \Delta_{2\gamma} \sigma_z \right)$$ with $\Omega_\text{eff} = \Omega_0\Omega_1/(2\Delta)$ (two-photon Rabi frequency), where typically $$\Omega_\text{eff} \approx 5.7 \times 10^7\,\mathrm{rad/s}$$ (9.1 MHz), single-photon detuning $\Delta \approx -1.52$ GHz, and $\pi$-pulse duration $\tau_\pi \approx 35\,\mu\mathrm{s}$.

Observed transfer efficiencies are $\chi_1\approx0.88$ for the splitter and $\chi_2\approx0.76$ for the recombiner, yielding a mean interferometer contrast $C=0.65$ (EMCCD detection) with peak values up to 0.80 for molecules near $v_0$.

4. Phase Evolution in Parallel Electric and Magnetic Fields

The first Raman $\pi/2$-pulse prepares $(|x\rangle+|y\rangle)/\sqrt{2}$. During propagation through regions of aligned electric ($E\hat{z}$) and magnetic ($B\hat{z}$) fields, the relative phase accumulated is

$$\phi = \frac{1}{\hbar} (\mu_B B - d_e E_\text{eff}) T,$$

with $\mu_B$ the Bohr magneton, $E_\text{eff} = \eta(E) E_\text{eff}^\text{max}$ ($E_\text{eff}^\text{max} = -26$ GV/cm for YbF, $\eta(20\,\mathrm{kV/cm})=0.693$, so $E_\text{eff}\approx-18$ GV/cm), $d_e$ the eEDM, and $T$ the interrogation time (typically $T=5\,$ms, for interaction length $0.77$ m at $v_0$).

After evolution, a second $\pi/2$ pulse maps this phase onto the hyperfine populations: $P_0 = \cos^2(\phi/2), \qquad P_y = \sin^2(\phi/2).$ The measured signal asymmetry $A\approx \cos(2\phi)$ is extracted after correcting for detection efficiency.

5. Detection: Efficiency, SNR, and Contrast

Detection is performed by state-selective microwave transfer ($F=1 \rightarrow N=1$ or $F=0 \rightarrow N=1$) followed by a cycling transition $N=1 \rightarrow A^2\Pi_{1/2}(v=0,J=1/2)^+$, with fluorescence detected on photomultiplier tubes (PMTs) or EMCCD cameras (Jenkins et al., 31 Jan 2026). The EMCCD provides overall detection efficiency $\epsilon_\mathrm{EM}\approx54\%$ (on $\sim10^6$ photons per shot), with weighted-mean fringe contrast $C=0.65$ and shot-noise-limited SNR $\sim10^3$ per shot. Crosstalk and background are quantitatively characterized ($x_A<0.002$, $x_B=0.030$; $P_\mathrm{bg}=2.33\%$).

Ultracold beam parameters ensure slow divergence and minimized dephasing, preserving high spatial and temporal contrast over several milliseconds of interrogation time (Alauze et al., 2021).

6. Sensitivity, Statistical Uncertainty, and Systematic Effects

The shot-noise-limited statistical uncertainty for an EDM measurement per shot is

$$\sigma_{d_e} = \frac{\hbar}{2 C E_\text{eff} T \sqrt{N_\text{mol}}}$$

For demonstrated parameters: $C=0.65$, $E_\text{eff}\approx18$ GV/cm, $T=5$ ms, $N_\text{mol}=2 \times 10^6$, and 5 shots/s (50% duty cycle), the expected daily sensitivity is $\sigma_{d_e} \approx 8.6\times10^{-30}\,e\,$cm, reaching $\sigma_{d_e} < 1 \times 10^{-30}\,e\,$cm in approximately 100 days (Jenkins et al., 31 Jan 2026). Systematic error contributions include field-reversal imperfections, spatial inhomogeneity, microwave leakage, Stark-shift stability, and optical pumping uncertainty.

Upgrades involving slower molecular beams (to increase $T$) and higher flux (enhancing $N_\text{mol}$) could yield $\sigma_{d_e} < 10^{-31}\,e\,$cm, approaching several orders of magnitude below current limits.

Parameter	Symbol	Value (Demonstrated)
Two-photon Rabi freq.	$\Omega_\text{eff}$	$5.7\times10^7\,\mathrm{rad/s}$
$\pi$-pulse efficiency	$\chi_{1,2}$	0.88, 0.76
Interrogation time	$T$	$5$ ms
Effective field	$E_\text{eff}$	$18$ GV/cm
Molecules/shot	$N_\text{mol}$	$2.0 \times 10^6$
Detection contrast	$C$	0.65

7. Extensions: Multilevel Spin Interferometry and “Magic” Trapping

Technologies underlying the two-level eEDM YbF interferometer facilitate extension to multilevel spin interferometry. By encoding “spin-1” in $|N=0,M_N=0\rangle$, $|N=1, M_N=+1\rangle$, and $|N=2, M_N=+2\rangle$ rotational states, and engineering laser trapping near a “magic” wavelength where differential polarizabilities are nullified, it is possible to achieve coherence times exceeding one second for all superposition states simultaneously (Hepworth et al., 2024). Generalized Ramsey sequences enable multiparameter estimation with Fisher information surpassing that of repeated two-level protocols. For YbF, the magic condition appears near $\lambda_\text{magic} \approx 1064.5$ nm with trap depths $\sim k_B \times 30\,\mu$K and negligible photon scattering rates.

These advances make possible high-visibility, second-scale coherent dynamics and three-level interferometric Ramsey fringes, opening applications in quantum metrology, quantum information encoded in high-dimensional qudits, and synthetic lattice dimensions (Hepworth et al., 2024). Readout is achieved via optical cycling, with rotational states mapped onto distinct fluorescence channels. The system thus serves as both a platform for fundamental searches (e.g., for $d_e$) and a general testbed for quantum-enhanced and multiparameter precision measurement protocols.