Resolved-Sideband Cooling of a Levitated Nanoparticle in the Presence of Laser Phase Noise

We investigate the influence of laser phase noise heating on resolved sideband cooling in the context of cooling the center-of-mass motion of a levitated nanoparticle in a high-finesse cavity. Although phase noise heating is not a fundamental physical constraint, the regime where it becomes the main limitation in Levitodynamics has so far been unexplored and hence embodies from this point forward the main obstacle in reaching the motional ground state of levitated mesoscopic objects with resolved sideband cooling. We reach minimal center-of-mass temperatures comparable to $T_{\min }=10\mathrm{mK}$ at a pressure of $p=3\times {10}^{-7}\mathrm{mbar}$, solely limited by phase noise. Finally we present possible strategies towards motional ground state cooling in the presence of phase noise.

Figure 1

Experimental setup. The nanoparticle levitates in a mobile optical tweezers trap (red), positioned in the center of the high finesse cavity field. A weak cavity light field (purple) observed on a photodiode (PDH) is used for Pound-Drever-Hall locking on the cavity resonance ${\omega }_{\mathrm{cav}}$. The cross polarized pump field (blue) is frequency modulated with an EOM at $\mathrm{FSR}+\mathrm{\Delta }$ and its transmission is recorded (PD). Standard PFC of the optical tweezer trap prevents particle loss and cross coupling between different degrees of freedom ($x$, $y$, $z$). A piezo stage allows for precise 3D positioning of the particle along the cavity axis. The collected trapping light is used in balanced forward detection.

Figure 2

Temperature versus pressure. (a) PSDs at various pressures ($p=0.3$, $3\times {10}^{-3}$, $3\times {10}^{-5}$, and $3\times {10}^{-7}\mathrm{mbar}$). The area of the PSD $⟨y^2⟩$ and therefore the temperature is reduced by reducing the pressure and applying cavity sideband cooling. (b) Applying cavity sideband cooling at optimal detuning $\mathrm{\Delta }=-{\mathrm{\Omega }}_y$ and intracavity power of $P_{\text{intra}}=75\mathrm{mW}$. $T_{\mathrm{c}.\mathrm{m}.}$ reduces linearly with decreasing pressure down to a stable $T_{\min }=35\mathrm{mK}$. Theory with negligible phase noise $S_{\varphi }=0{\mathrm{Hz}}^2/\mathrm{Hz}$ (solid line) predicts a monotonic linear decrease in $T_{\mathrm{c}.\mathrm{m}.}$ with pressure. Theoretical predictions assuming phase noise of $S_{\varphi }=2\pi \times 4{\mathrm{Hz}}^2/\mathrm{Hz}$ (half-solid line) tails off to a stable final temperature $T_{\mathrm{th}}=34\mathrm{mK}$. Shaded area assumes a phase noise regime from half to twice the value of $S_{\varphi }$.

Figure 3

Temperature versus detuning $\mathrm{\Delta }$ for different input powers $P_{\mathrm{in}}$. At high pressures (a)–(d) clear optimal detuning ${\mathrm{\Delta }}_{\mathrm{opt}}\approx -{\mathrm{\Omega }}_m$ is observed. At low pressures (e)–(h) the temperature minimum is washed out. Theory assuming $S_{\varphi }=0{\mathrm{Hz}}^2/\mathrm{Hz}$ (solid line) predicts stronger cooling with increasing $g$. Theory assuming $S_{\varphi }=2\pi \times 4{\mathrm{Hz}}^2/\mathrm{Hz}$ (half-solid line) accounts for phase noise. The shaded area assumes a phase noise regime from half to twice the value of $S_{\varphi }$. In (d) and (h) $T_{\mathrm{c}.\mathrm{m}.}$ at optimal detuning versus $P_{\mathrm{in}}$ is depicted, showing at low pressure the opposite behavior in comparison to high pressure.

Figure 4

Temperature versus particle position $y$ at optimal detuning $\mathrm{\Delta }=-{\mathrm{\Omega }}_m$ and various intracavity powers $P_{\text{intra}}$. (a) At high pressures, $T_{\mathrm{c}.\mathrm{m}.}$ changes sinusoidally with position. The minimal temperature of $T_{\min }\approx 50\mathrm{K}$ agrees well with theory (solid line). The maximum temperature deviates from the theory prediction due to the movement of the particle in the cavity field, as discussed in the main text. (b)–(d) $T_{\mathrm{c}.\mathrm{m}.}$ at low pressures. For the lowest power (b) $T_{\mathrm{c}.\mathrm{m}.}$ keeps its sinusoidal dependence on $y$ with a minimal temperature $T_{\min }\approx 10\mathrm{mK}$. The position dependence is gradually lost and the minimum temperature increases, when the intracavity power is raised. Theory neglecting phase noise contributions with $S_{\varphi }=0{\mathrm{Hz}}^2/\mathrm{Hz}$ (solid line) consistently predicts a sinusoidal dependence on position $y$. Theory assuming a phase noise level of $S_{\varphi }=2\pi \times 4{\mathrm{Hz}}^2/\mathrm{Hz}$ (half-solid line) accounts for phase noise and for the additional SNRP due to the trap (dotted line). The shaded area assumes a phase noise regime from half to twice the value of $S_{\varphi }$.