Towards Quantum Gravity Measurement by Cold Atoms

Transcription

1 Towards Quantum Gravity Measurement by Cold Atoms SUPA, RAL, Sonangol, IMechE, IOP Quantum Gravity and Gauge Group University of Aberdeen University of Nottingham Quantum Fields, Gravity & Information

2 Content 1. Quantum Gravity observation difficulties. Probing Spacetime with cold atoms 3. Quantum mechanical and Thomas-Fermi approach 4. Mechanism of Observation (Experiment)

3 Quantum Gravity Observation Difficulties Paradoxical but Possible Impossibility Relativity and Ascending & Descending by M.C.Escher

4 Quantum Gravity Observation Difficulties 1 R Rg 8 GT cm GeV s i ( r, t) ( V ( r, t)) ( r, t) t m GeV

5 Probing Spacetime with cold atoms The ideal is based on a seemingly Lamb shift of cold atoms centre of mass induced by gravitational Perturbation. In 011 Charles H.-T. Wang & Collaborators proposed probing Spacetime by cold atoms Electron energy Level shifts Cold atoms or BEC - Proton oscillates due to vacuum + fluctuations of EM field Indirect Observation of Spacetime fluctuation created by a binary star system Lamb Shift of Hydrogen atom

6 Probing Spacetime with cold atoms Cold atoms Laser with the same frequency as the atoms resonance frequency slow down atoms to temperature of microkelvin range, i.e. COLD ATOMS. Evaporative cooling extract high kinetic energy atoms, and further lower the Temperature to nanokelvin forming BOSE EINSTEIN CONDENSATES Animation from Absolute zero

7 Probing Spacetime with cold atoms From FDT, quadruple radiation of a particle and damping reach thermal equilibrium with stochastic Gravitational wave background. Quadruple oscillation sequence Where E T 3G hij hij E ( ) 5 0 T d c the Planck spectral density with T 0 BEC nd derivative of its 1 st order standard deviation due to spacetime fluctuation (1) i d x () t 3 vt dt 9 p 16 x () t r t p 9 (1) i ( ) E T V 1 kt e 1 16 m 7 p 3 L m E 4 10 N 0.5% ( L / m) 3 9 3

8 Quantum Mechanical Approach Considering a 1D harmonic oscillator perturbed by a potential V(x,t), the Hamiltonian is given as H ˆ H ˆ V ( x, t ) 0 Where V( x, t) ma( t) x and A( t) A sin( t) 0 V 16 m 7 p 3 L m VV( t( ') t ') m ma n( tv )( nx, tx) i ni ni With expected value of position of the particle as n x i n a a i m ˆ ˆ

9 Now the 1 st order perturbation Coefficient of probability expressed as c (1) ni (t) = - im n x i A t (w ni ) The mean power spectral density is Quantum Mechanical Approach 1 S A A t ni * t ( ni ) t ( ni ) t ( ni ) The Transition probability is found to be m P n x i S t ( ) ni V 16 m 7 p 3 L m To calculate the total power absorbed by the particle Power spectral density can be given as ma0 P ( ) 4 A0 S( ) [ ( ) ( )] P ma 4 3

10 Thomas-Fermi Approach Using a Rb87 BEC the GPE is given ( Xt, ) 4 as i ( V ( X, t) T ( X, t) ) ( X, t) t m m The total trap potential includes the Mechanical induced oscillation 1 V ( X, t) ma( t) z m X x, y, z a X Thomas-Fermi approximation is used when Kinetic term in GPE is less than interaction n TF V ( x, t) g n g Constant ratio of 1 for small perturbation low 1Hz, 10^8, 1mm n TF n 1

11 Thomas-Fermi Approach The same treatment was given to high frequency, and amplitude. There were observed perturbations on the ratio due to the mechanically induced oscillation. Constant ratio of 1 for small perturbation low 1KHz, 10^6, 1cm Constant ratio of 1 for small perturbation low 1KHz, 10^3, 1cm At KHz, 10^6 TF approximation fails

12 Experimental Setup

13 Experimental Apparatus Status

14 Experimental Apparatus Status

15 Experimental Apparatus Status

16 Thank You Acknowledgements Dr Charles Wang, Martin Caldwell, Teodora Oniga, Andrew Mcleman, Sonangol, RAL, University of Aberdeen, University of Nottingham, University of Birmingham, and SUPA for guidance, collaboration, support and opportunities References: [1] Wang, C.H.-T., Bingham, R. And Mendonca, J.T. 01 Probing Spacetime fluctuations using cold atoms traps. arxiv: [] Dos Santos, M. M., et al.,013 Toward Quantum Gravity Measurement by Cold Atoms Journ. Plasma Phys. Cambridge University press. doi: /s