A levitated nanocryostat: Laser refrigeration, alignment and rotation of Yb3+ : YLF nanoparticles A. T. M. Anishur Rahman & Peter F. Barker Department of Physics & Astronomy University College London London, UK

Outline UCL optomechanics – an overview Introduction to laser cooling Motivation behind laser refrigeration Cooling the internal temp. of levitated Yb3+:YLF nanocrystals Birefringence of Yb3+:YLF - Rotation in CP light and alignment in LP light Parametric feedback cooling Conclusions

Main objective of our experiments Creating/Generating different non- classical states such as – the motional ground states Schrodinger cat states

Main challenge - decoherence1 High CM temperature <𝑛> = 𝑇 𝐶𝑀 ℎ𝜔 Quantum system Collision with background gas 𝜏𝑔=ℎ𝜔/𝛾𝑔𝑘𝐵𝑇𝑐𝑚 Recoil heating 𝜏𝑟∝1/𝐼 Blackbody emission ∝𝑇5 1. Chang et al. PNAS 2010.

UCL Optomechanics Experiments Dipole trap Hybrid trap Paul trap Creating non-classical states i.e. motional ground state Dipole trap Laser refrigeration, parametric feedback cooling Hybrid trap Cavity + Paul trap Cavity cooling Paul trap Nanodiamond with NV centres

Laser refrigeration Controlling the internal temperature of a material using laser only Similar to laser cooling of atoms but it uses anti-Stokes fluorescence for controlling the internal temp

Laser refrigeration -motivations Enabling fundamental physics experiments i.e. by increasing the spin coherence time of NV centres in appropriately engineered levitated nanodiamond Solving existing problems of burning/melting of nanoparticles in dipole trap1,2,3 Rahman et al. Sci. Rep. (2016). Millen et al. Nat. Nano. (2014). Hoang et al, Nat. Comm. (2016)

Conditions for optical refrigeration Anti-Stokes fluorescence (λf< λ) Energy gap between levels ∆𝐸<𝑘𝐵𝑇 High quantum efficiency Phonon energy of host materials must be low < kBT Rapid thermalization of population in excited state (normally in ps) Excited state lifetime should be longer than thermalization time λ λf

Anti-Stokes fluorescence from levitated Yb3+: YLF nanocrystals

Internal temp. of levitated Yb3+:YLF naonocrystals Temp. from Boltzmann distr. - 1 𝑇 = 1 𝑇0 + 𝑘𝐵 ∆𝐸65 ln 𝑅 𝑅0 , where 𝑅= 𝐼(𝐸6 →𝐸1) 𝐼(𝐸5 →𝐸2) @ T and 𝑅0= 𝐼(𝐸6 →𝐸1) 𝐼(𝐸5 →𝐸2) @ T0 A. T. M. A. Rahman and P. F. Barker, Nat. Photon. (2017).

A. T. M. A. Rahman and P. F. Barker, Nat. Photon. (2017). Temperature from PSD Power spectral density – 𝑆 𝑥 (𝜔)= 2𝑘𝐵𝑇 𝑀 𝛾 𝜔2−𝜔02 2+𝛾2𝜔2 Temperature and damping are related as - 𝑇∝ 𝛾2 Assuming T1064 nm= 255 K, 𝑇 1031 𝑛𝑚 = 𝑇 1064 𝑛𝑚 𝛾 1031 𝑛𝑚 2 𝛾 1064 𝑛𝑚 2 =171±21 K A. T. M. A. Rahman and P. F. Barker, Nat. Photon. (2017).

Blackbody emission and it’s consequence Plank’s law of blackbody emission 𝐼 𝜔 = ℎ𝜔3 𝜋2𝑐2( 𝑒 ℎ𝜔 𝑘𝐵𝑇 −1) Damping rate due to blackbody emission - 𝛾𝐵𝐵 ∝(𝑅BB/𝜔𝑚 ) where 𝑅𝐵𝐵= 𝐼 𝜔 𝑑𝜔 . Number of oscillations before the oscillator excites by one quanta – 1/𝛾𝐵𝐵 ∝(𝜔𝑚/𝑅BB )

Given right laser and proper nanoparticles We can reach 50 K which is about 4 orders magnitude blackbody suppression

Thermodynamic simulation Heating rate due to collisions with gas molecules – 𝑞 ℎ = 8𝜋 𝑎 2 𝑘 𝑔 2𝑎+Λ𝐺 ∆𝑇, where a is the radius, Λ is the mean free path of air molecules, kg is thermal conductivity of air, G=(18γ-10)/A(γ+1) , A is the accommodation coefficient of air and ∆𝑇 is the difference in temperature between the air molecules and levitated particles. Cooling rate due to anti-Stokes fluorescence - 𝑞 𝑐 =𝑉𝛼𝐼(1−η𝑞 λ λ𝑓 ), where V is the volume of the nanoparticle, 𝛼 is the absorption coefficient, I is the laser intensity, η𝑞 quantum efficiency, λ𝑓 is the average fluorescence wavelength and λ is the excitation wavelength. Setting qh=qc at equilibrium, we get T≈200 K A. T. M. A. Rahman and P. F. Barker, Nat. Photon. (2017).

Birefringence of Yb3+:YLF : self orientation Two orientations a // E & c // E Fluorescence and temp. depends on crystal orientation Trapping power > 50 mW : c // E Trapping power < 50 mW : a // E A. T. M. A. Rahman and P. F. Barker, Nat. Photon. (2017).

Birefringence of Yb3+:YLF - rotation & pendular motion3 Pendular motion in linearly polarized light (Fig. a & d) Rotation in circularly polarized light (Fig. b & c) ATM A. Rahman and P. F. Barker, Nat. Photon. (2017).

Parametric feedback cooling It controls the CM motion of a levitated nanoparticle Has been successfully used to reach sub-millikelvin CM temperature1 Ground state how far or is it needed???

Joint CM & internal temperatures control Work in progress

Conclusions Internal temperature can be controlled using anti- Stokes fluorescence Internal temperature as low as 130 K has been achieved. Blackbody emission has been suppress by approx. four orders of magnitude Birefringent Yb3+:YLF particles rotate in CP & LP light