Coherence limits in lattice atom interferometry at the one-minute scale

Abstract

In quantum metrology and quantum simulation, a coherent non-classical state must be manipulated before unwanted interactions with the environment lead to decoherence. In atom interferometry, the non-classical state is a spatial superposition, where each atom coexists in multiple locations as a collection of phase-coherent partial wavepackets. These states enable precise measurements in fundamental physics and inertial sensing. However, atom interferometers usually use atomic fountains, where the available interrogation time is limited to around 3 s for a 10 m fountain. Here we realize an atom interferometer with a spatial superposition state that is maintained for as long as 70 s. We analyse the theoretical and experimental limits to coherence arising from collective dephasing of the atomic ensemble. This reveals that the decoherence rate slows down markedly at hold times that exceed tens of seconds. These gains in coherence may enable gravimetry measurements, searches for fifth forces or fundamental probes into the non-classical nature of gravity.

Extended data

Extended Data Fig. 1 Atoms load into integer multiples of the lattice period.

a, Fourier spectral decomposition components of the measured fringes as a function of separation. Yellow represents a higher power density at the specific fringe frequency. b, fringe data when the initial wavepacket separation equals 7.5 lattice sites and fit (solid line) to a sum of two sine functions with frequencies corresponding to separations of 7 and 8 lattice sites. This data suggests that the lattice enacts a second beam splitter, such that the partial atomic wavepacket loads evenly into adjacent lattice sites with 7 and 8 lattice site separations.

Extended Data Fig. 2 Measured interferometer fringe frequency vs scan parameter.

a, fringe frequency from propagation, ω_prop, obtained by scanning the hold time τ. b, fringe frequency from laser interactions, ω_L, obtained by scanning the pulse separation T. Error bars correspond to 1σ (68%) Gaussian confidence intervals. Red lines correspond to the expected analytical fringe frequency as shown by equations (9) and (10). c, Contrast loss as a function of separation time, T. The fitted interferometer contrast varies as a function of T with a fast sinusoidal component given by lattice spacing times the recoil velocity, λ_latt/2·v_r. In addition, the contrast decay curve exhibits a smaller amplitude (4% typically) sinusoidal component with periodicity given by the least common multiple of the lattice laser and tracer laser wavelengths, λ_latt and λ_tracer, which is due to dephasing from the interference of the lattice and tracer lasers. The red line fits the data using free parameters for the amplitudes of the exponential decay, amplitude of the higher frequency sinusoidal function and the amplitude of the lower frequency variation.

Extended Data Fig. 3 Noise and sensitivity.

a, Measured atom number, N, as a function of hold time, τ. This dataset was taken with trap depth U₀ ≈ 12 E_r. The solid line shows a fit to a decaying exponential. b, Sensitivity and standard quantum limit noise. The measured acceleration sensitivity within one second of measurement time ($\delta g/g/\sqrt{{\rm{Hz}}}$) is shown as dots. Values corresponding to the estimated standard quantum limit (shot) noise are calculated from the measured contrast and atom numbers and shown as solid lines.

Extended Data Fig. 4 Simulations of the t-test statistic, $\hat{{C}}/{{\sigma }}_{\hat{C}}$.

a. Histogram of the distribution of $\hat{C}/{\sigma }_{\hat{C}}$ for 1000 simulated fringes with zero contrast C = 0. b. Cumulative distribution functions (cdf) for $\hat{C}/{\sigma }_{\hat{C}}$, shown for varying levels of simulation added noise (blue – compatible with experiment imaging and shot noise, yellow-10 times larger, green-10 times smaller).

Extended Data Fig. 5 Loading fractions.

Experimental data showing fractions of atoms remaining after loading and 1 second of hold time as a function of initial number, shown vs a, global tilt angle and b, trap depth, U₀. Experimental data is shown by blue dots with error bars corresponding to 1σ (68% confidence) Gaussian intervals, and simulation results are in green.

Extended Data Fig. 6 Phase shifts due to differential motion between the atomic wavepacket in the top and bottom lattice sites.

The atomic wavepacket (wavy line on top of grey disk) is split into an equal superposition of two partial wavepackets (wavy lines on top of purple and orange disks). The partial wavepackets are loaded into lattice sites (blue ovals) that are spatially separated by a distance of Δz. Solid lines show representative atom trajectories in the two lattice sites, which are both initially loaded at position {x, y}_i and start with phase ϕ₀. Survival probabilities due to Landau-Zener tunneling are shown by the trajectories color gradients and range from 1 (green) to 0 (red). Time-dependent tilts cause the position of the lower lattice site to oscillate with a differential amplitude relative to the top in the transverse plane, a_tilt, leading to a displaced trajectory of the bottom atom partial wavepacket with final position ${\{x,y\}}_{f}^{t}\ne {\{x,y\}}_{f}^{b}$ (difference Δ{x, y}_sep) and propagation phase difference ${\phi }_{f}^{t}\ne {\phi }_{f}^{b}$. The rightmost panels show the two main dephasing mechanisms, due to differential propagation phase, $\Delta {\phi }_{\text{latt}}^{\text{prop}}$, and separation phase, $\Delta {\phi }_{\text{latt}}^{\text{sep}}$.

Extended Data Fig. 7 Simulated contrast decay.

Contrast vs hold time τ for four separate configurations: standard level of vibrations, with vibrations reduced to zero, with tunneling reduced to zero, and with atom position and velocity distributions widths reduced 5-fold. All simulations used a wavepacket separation of $\Delta z=1.9 \, \mu \text{m}$ and a peak trap depth of U₀ = 7 E_r. The dashed lines represent exponential fits to the τ < 20 s region of the data. The bands represent 95 % confidence intervals.

Extended Data Table 1 Long τ fringe datasets parameters

Extended Data Table 2 Investigating the cause of contrast decay

Extended Data Table 3 Simulation parameters