Compact vacuum levitation and control platform with a single 3D-printed fiber lens

Abstract

Levitated dielectric particles in a vacuum have emerged as a new platform in quantum science, with applications ranging from precision acceleration and force sensing to testing quantum physics beyond the microscopic domain. Traditionally, particle levitation relies on optical tweezers formed by tightly focused laser beams, which typically require multiple bulk optical elements aligned in free space, limiting robustness and scalability of the system. To address these challenges, we employ a single optical fiber equipped with a high numerical aperture (NA) lens directly printed onto the fiber facet. This enables a compact yet robust optical levitation and detection system composed entirely of fiber-based components, eliminating the need for complex alignment. The high NA of the printed lens allows stable single-beam trapping of a dielectric nanoparticle in a vacuum, even while the fiber is in controlled motion. The high NA also allows for collecting scattered light from the particle with excellent collection efficiency, thus enabling efficient detection and feedback stabilization of the particle's motion. Our platform paves the way for practical and portable sensors based on levitated particles and provides simple yet elegant solutions to complex experiments requiring the integration of levitated particles.

Figures (10)

• Figure 1: Vacuum levitation of a nanoparticle using a high NA fiber lens.a, Illustration of a compact, fiber-based, single-beam tweezer platform. A 1064 nm laser source is coupled to a single-mode fiber connected to the input port of a fiber optic circulator. The circulator's output port is spliced to a fiber with a diffractive lens directly printed onto the fiber facet. The laser beam exiting the fiber core is first expanded by a no-core part and reaches the diffractive Fresnel lens at the end. The lens tightly focuses the expanded beam to a focal spot at around $34~\mu m$ from the lens, forming an optical trap. Scattered light from the trapped particle is collected by the lens, coupled back into the fiber, and then redirected to a detector via the circulator, enabling efficient detection of the particle's motion. The inset depicts the scanning electron microscope image of the lens front, with a scale bar of $50~\mu m$. b, Side view of the fiber tweezer captured by a commercial CMOS camera (see Fig. \ref{['fig4']}). A silica nanoparticle with a diameter of $142~nm$ is trapped at the focus at a pressure of $\sim 0.3~mbar$.
• Figure 2: Fiber-based detection of the particle's displacement.a, Schematics of the experimental platform. The laser field launched from the input port of the circulator and guided to the fiber lens to trap a particle. The light scattered off the particle by the trapping beam is collected by the same fiber lens and redirected to the detector (smaller wavy arrows). The particle's displacement is encoded in the phase of the scattering field. In the meantime, a small fraction of the trapping beam also reflects off the interfaces of the lens elements (larger wavy arrows) and interferes with the scattering field, serving as a local oscillator. The interfered signal is then recorded by the fiber-coupled amplified photo-detector with a gain of $1.23 \times 10^4~V/W$. b, Power spectral density (PSD) of the measured signal. The PSD shown here is obtained by averaging the PSDs of twenty individual time traces of the length $\sim 28~ ms$ (one example shown in the inset) measured consecutively. The particle's oscillatory motion along the optical axis appears as a prominent peak at $\Omega_{z}/2\pi = 69.2~kHz$ as well as its higher harmonics.
• Figure 3: Extraction of the particle dynamics from the measured signal.a, Typical time trace of the detected signal measured at a pressure of $0.3~mbar$. The particle's displacement along the z-axis leads to modulation of the phase of the scattering field, resulting in the intensity modulation of the interference field. In addition, other parameters, such as the relative phase between the reflected field and the scattering field, also exhibit slow fluctuations, contributing to the additional fluctuation of the measured signal. b. Examples of the time trace segments of $\approx 72~\mu s$ in length, zoomed in from panel b at different times (shown in blue and green). Solid lines are the results of the fitting to Eq. \ref{['eq_int']}, assuming the particle undergoes a coherent oscillation during the period. c-e, Trends of reflected field intensity $\mathbfcal{I}_{r}$ (c), relative phase $\varphi_{rel}$ (d), and intensity of the reflected field in orthogonal polarization $\mathbfcal{I}_{r,\perp}$ (e). Fluctuations are observed for all parameters. f, The distribution of the particle's displacement power $z^2$ extracted from the fittings. The distribution follows the Boltzmann probability distribution, a characteristic of the thermal state. The root-mean-square value is $\sqrt{\langle{z^2}\rangle } \approx 89.89~nm$, showing excellent agreement with the theoretical value of $\sqrt{\langle{z^2}\rangle}_{theory} \approx 89.61~nm$ obtained from the equipartition theorem.
• Figure 4: Cold damping of the particle's motion in high vacuum.a, Schematic representation of the fiber-based setup including the feedback scheme. The detected signal is processed with an FPGA, which is digitally filtered to generate an output feedback signal. This signal is sent to an electrode located a few millimeters from the lens. This signal creates an electric field, between the electrode and grounded fiber holder (FH) that exerts a Coulomb force proportional to the particle's position with a phase delay optimized to damp the particle’s motion along the z-axis. b, A time trace of the detected signal at the pressure of $1.3 \times 10^{-4} mbar$ when the feedback force is off (red) and on (blue). When the feedback is turned on, an immediate decrease in the signal amplitude is observed, indicating the corresponding decrease in the particle's oscillatory motion. The insets show exemplary zoomed-in segments with the length of $100~\mu s$ with the feedback off (left) and on (right). c, Normalized statistical distributions of $\varphi_{rel}$ (left) and $\mathbfcal{I}_{r,\perp}$ (right) extracted from the measured signal over a duration of $\sim 85~ms$ until feedback is on. The mean values of $\varphi_{rel}$ and $\mathbfcal{I}_{r,\perp}$ are used as constant parameters in Eq. \ref{['eq_int']} when converting the signal during the cooling phase to the particle's displacement. The standard deviations are $\sigma_{\varphi} \sim 1.73^{\circ}$ and $\sigma_{\mathbfcal{I}_{r,\perp}} \sim 30~mV$, respectively. d, Inferred particle's displacement during the cooling phase. The inset shows the PSD of the converted displacement signal around the particle's oscillation frequency of $\Omega_z/2\pi \approx 70.3~ kHz$. We perform the areal integration of the PSD around $\Omega_z$ to obtain the root-mean-squared value of the particle's displacement $z_{rms} = \sqrt{\langle z^2\rangle}\approx 2.26~nm$ and the corresponding effective mode temperature of $T_{CoM} = 193~mK$.
• Figure 5: Stability of a fiber lens holding a levitated nanoparticle in vacuum.a, The fiber lens and the levitated particle are monitored during the transport process with an additional imaging system. Using this system, we record a video while the fiber is being moved along the y-axis. b, Selected frames of a recording show the fiber and particle's position at times of $t = 1.7$, $2.8$, and $3.8~s$ (from left to right). In these frames, the particle is moved with a velocity of $\sim 130~\mu m/s$ (see Visualization 1). Arrows and red circles highlight the location of the particle in each frame. They show the particle is stably locked with the fiber while the fiber is being moved. c, The particle in our fiber-based trap is continuously monitored at a pressure of $1.3\times10^{-4}~mbar$ for more than six hours. During the measurement, the particle was left without any feedback-based stabilization.