Quantum-droplet interferometry

TL;DR

The paper addresses how quantum droplets (QDs) can enable robust matter-wave interferometry by balancing mean-field and beyond-mean-field interactions. It develops barrier-based interferometers in harmonic-oscillator and ring traps, analyzes 50:50 splitting via barrier height, and uses post-recombination atom-number imbalance to read out the interferometric phase, with additional demonstrations of tilt-metry, target detection, and Sagnac rotation sensing. Performance is controlled by the atom number $\mathcal{N}$ and the relative MF strength $\gamma$, with optimal operation near the QD-HO crossover and a trade-off between high contrast and high sensitivity depending on the application. The work highlights the potential of 1D QDs for precise sensing, offering routes to tilt meters, compact rotation sensors, and target detectors, while outlining experimental challenges and directions for future study, including quantum-statistics effects via truncated-Wigner methods.

Abstract

We propose atom interferometers based on quantum droplet (QD), which is also being reported as a superior platform for interferometry. The emphasis has been given to harmonic-oscillator (HO) or ring-shaped potentials. In the HO trap, a Gaussian barrier induces coherent splitting; in the ring, one or two barriers guide the splitting and subsequent recombination. The atom number and relative mean-field interaction strength critically affect the interferometric performance. The transmission-coefficient analysis identifies values of the barrier parameters for the balanced $50:50$ splitting. The post-recombination atom-number imbalance serves as a sensitive indicator of the relative phase between merging daughter QDs. We demonstrate that the HO-based setup may serve as a tilt-meter and target detector, and the ring geometry may be used as a compact QD Sagnac interferometer for rotation sensing.

Figures (15)

• Figure 1: The maximum density of the free-space QD solution (Eq. \ref{['QDsol']}), $n_{max}\equiv|\psi(x=0)|^2$, as a function of the normalized chemical potential $\bar{\mu}\equiv \mu /\mu _{0}$ ($\mu _{0}$ is the critical chemical potential) for $\gamma =1$. Insets (a)-(e) exhibit the QD density profiles corresponding to $\bar{\mu}=0.05$, $0.33$, $0.67$, $1-10^{-10}$ and $1-10^{-14}$, respectively. In this case, $x$ and $t$ are mesured in units of $l_{\perp}=0.72\;\mathrm{\mu }$m and, $1/\omega _{\perp }=0.32\;$ms, respectively.
• Figure 2: (a) The dependence of the RMS width, $\sigma$, of the free-space QD solution (\ref{['QDsol']}) on the normalized chemical potential for fixed values of the relative MF interaction strength $\gamma$. (b) The dependence of $\sigma$ on $\gamma$ for fixed values of the atom number $N$. In this case, $x$ is measured in units of $l_{\perp}=0.72\;\mathrm{\mu}$m, $t$ in units of $1/\omega _{\perp }=0.32\;$ms, and $N=1$ corresponds to $1.8\times 10^{4}$ atoms.
• Figure 3: The comparison of the QD density profiles for $\gamma =1$, as obtained from the numerical solution and produced by the TF approximation (\ref{['TF']}) under the action of the HO potential, for different norms: (a) $N=5$, (b) $N=10$, (c) $N=25$, (d) $N=50$, (e) $N=75$, (f) $N=100$. Here, the frequency of the HO trap is $\omega_{x}=0.1\omega_{\perp }$, $x$ is measured in units of $l_{\perp }=0.72\;\mathrm{\mu }$m, $t$ in units of $1/\omega _{\perp }=0.32\;$ms ,and $N=1$ corresponds to $1.8\times 10^{4}$ atoms.
• Figure 4: (a) The chemical potential $\mu \ $vs. the norm $N$ for different values of $\gamma$, in the presence of the HO potential. Here, we dsitinguish two regions: the QD area for $\mu <0$ and the TF region for $\mu >1$, which are separated white region of weakly nonlinear states. Dotted line are $\mu (N)$ dependences obtained in the TF limit. (b) The RMS widths vs. $N$, for different values of $\gamma$. Here, the frequency of the HO trap is fixed as $\omega _{x}=0.1\omega _{\perp }$. $x$ is measured in units of $l_{\perp }=0.72\;\mathrm{\mu }$m, $t$ in units of $1/\omega _{\perp }=0.32\;$ms, $\mu$ in the unit of $\hbar \omega _{\perp }$, and $N=1$ corresponds to $1.8\times 10^{4}$ atoms.
• Figure 5: (a) The schematic of the QD interferometer based on the HO trap. (i) The prepared ground state is displaced by distance $x_{0}$ and released to move freely. (ii) Splitting of the moving QD by the central Gaussian barrier, (iii) and (iv) Recombination of the daughter droplets at the barrier. (b) The space-time trajectory of the interferometric sequence. (c) Dependences of the transmission coefficient on the barrier's height for different initial displacements of the QD, $x_{0}=90,\;100$, and $110$, are indicated by lines with squares, triangles and circles, respectively. (d) The sensitivity of the relative atom number, past the recombination, to the barrier's position. Here, the frequency of the harmonic trap is $\omega _{x}=0.1\omega _{\perp }$ and the width of the Gaussian barrier is $d_{0}=0.25$. The droplet is prepared with $\gamma =3$ and $N=0.5$. Coordinate $x$ and time $t$ are measured in units of $l_{\perp}=0.72\;\mathrm{\mu }$m and $1/\omega _{\perp }=0.32\;$ms, respectively.