Local optical potentials for ultracold atoms

Bodo Kaiser, 19.01.19

Introduction

Many body spin states

  • $c_1\mid\uparrow\rangle+c_2\mid\downarrow\rangle$
  • $c_1\mid\uparrow\uparrow\rangle+c_2\mid\uparrow\downarrow\rangle+c_3\mid\downarrow\uparrow\rangle+c_4\mid\downarrow\downarrow\rangle$
  • $c_1\mid\uparrow\dots\uparrow\rangle+c_2\mid\uparrow\dots\uparrow\downarrow\rangle+\dots+c_{2^n}\mid\downarrow\dots\downarrow\rangle$

Quantum complexity

  • $n$ particles
  • $2^n$ states
  • $2^{2n}$ matrix elements

Quantum simulator

Nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical.

Feynman, 1982

Optical potentials

Experimental setup

Requirements

  • time scale (< 10 μs)
  • focus spot size (< 1 μm)
  • deflection angle (> 50 μm)

Acousto-optic deflector

schematic of the acousto-optic deflector
  • position offset:
  • transmission efficiency:
  • $x\propto f_h, y\propto f_v$
  • $T\left(U_h, U_v, f_h, f_v\right)$

Optical deflection setup

schematic of the optical deflection setup

Optical imaging setup

schematic of the optical imaging setup

Experimental results

Beam profile

intensity distribution of truncated Gaussian beam near focal point

Text projection

intensity distribution of text projection

Transmission efficiency distribution

transmission efficiency distribution of 2D frequency sweep

Transmission efficiency optimization

transmission efficiency optimization using amplitude modulation

Summary and outlook

Summary

  • successful proof of concept in the creation of arbitrary potentials
  • transmission efficiency depends nonlinearly on RF signal
  • transmission efficiency variance was reduced
  • used signal source is limited

Outlook

  • improve transmission efficiency optimization
  • improve signal source (i.e. FPGA)
  • evaluate other deflector types (i.e. EODs)

Supplemental material

Caesium apparatus

schematic of the caesium experiment apparatus

Transmission efficiency optimization

transmission efficiency optimization using amplitude modulation