Igor Pikovski Experim rimental S l Searc rch for or Quant ntum - PowerPoint PPT Presentation

Igor Pikovski Experim rimental S l Searc rch for or Quant ntum um G Gravity SISSA SA/ISA ISAS, S, Tri ries este, , Ita taly 01.09.2014

High-energy scattering experiments High-precision quantum metrology Novel systems, that allow for precision measurement in a „quantum gravtitational“ paramter regime? Astrophysics and cosmology

 Measurable effects of classical gravity in Quantum mechanics quantum mechanics on fixed background space-time  Time dilation in quantum mechanics  Universal decoherence due to gravitational time dilation I. Pikovski, M. Zych , F. Costa, Č. Brukner. Univ iversal al Decp ecpherence ce due to Grav ravit itat atio ional al Tim ime Dilat ilatio ion. arXiv:1311.1095 (2013).  Pulsed quantum opto-mechanics Quantum gravity phenomenology  Opto-mechanical scheme to experimentally test possible quantum gravitational deformations of the center-of-mass canonical commutator I. Pikovski, M. Vanner, M. Aspelmeyer, M. S. Kim, Č. Brukner. Probing Pr ng Pl Planc nck-Scale ale P Phys ysic ics wit ith Quant ntum Optics cs. . Nature Physics 8, 393 (2012); arxiv:1111.1979. Outline

Yes! 𝐼 𝑗𝑗𝑗 = 𝑛𝑛𝑛 Earth’s gravity affects matter waves. Aharonov-Bohm-type phase due to the Newtonian gravitational potential: Δ𝜚 = 𝑛𝑛𝑛𝑛 / ℏ Tested with: Neutron interferometry  e.g. R. Colella, A. W. Overhauser, S. A. | 𝜔⟩ = 1 | 𝜔 𝑒𝑒𝑒𝑒 ⟩ + 𝑓 −𝑗Δ𝜚 | 𝜔 𝑣𝑣 ⟩ Werner, PRL 34, 1472-1474 (1975) 2 Atomic fountains  e.g. H. Müller, A. Peters, S. A. Chu, Δ𝜚 = 𝑛𝑛𝑛𝑛 / ℏ Nature 463, 926-929 (2010) Our w r work rk: I Incorp rporate t tim ime d dila ilation in into desc scription o of QM syst systems Time dilation in QM

2 𝑣 𝜈 𝑣 𝜈 = − 𝐼 𝑠𝑠𝑠𝑗 = 𝐼 𝑣 𝑗 , 𝑛 𝜈𝜈 , 𝐼 𝑠𝑠𝑠𝑗 = 2 + 𝑛 𝑗𝑗 𝑑 2 𝑣 𝑗 𝑣 𝑗 𝑑𝑣 0 = 𝐼 −𝑛 00 𝐼 𝑠𝑠𝑠𝑗 , 𝑑 2 low-energy limit: composite systems: 𝐼 𝑠𝑠𝑠𝑗 = 𝐼 0 + 𝑛𝑑 2   𝑗ℏ 𝜖 𝜖𝜖 | 𝜔⟩ = 𝐼 𝑠𝑠𝑠𝑗 | 𝜔⟩ internal remaining dynamics static part Hamiltonian in the weak-field limit 𝑃 ( 𝑑 −2 ) : 2𝑛 + 𝑛Φ 𝑛 + 𝑛Φ 2 𝑛 𝐼 0 + 𝑛𝑑 2 + 𝑣 2 𝑣 4 𝑣 2 𝑗ℏ 𝜖 8 𝑛 3 𝑑 2 + Φ 𝑛 2 𝑛 2 𝑑 2 𝐼 0 | 𝜔⟩ 𝜖𝑛 | 𝜔⟩ = − − 2 𝑑 2 𝑑 2 QM on fixed (classical) Coupling between internal background space- and external d.o.f. time with time dilation Gravitational part of interaction 𝐼 𝑗𝑗𝑗 = 𝑛𝑛 with Φ 𝑛 = 𝑛𝑛 : 𝑑 2 𝐼 0 Time dilation in QM

𝐼 ≈ 𝑛𝑛𝑛 + 𝐼 0 + 𝑛𝑛 𝑑 2 𝐼 0 Classically: Quantum mechanically: General relativity entangles any clock to the path due to gravitational time dilation. | 𝜔⟩ = 1 < 1 | 𝜔 𝑒𝑒𝑒𝑒 ⟩ | 𝐷 𝑒𝑒𝑒𝑒 ⟩ + 𝑓 −𝑗Δ𝜚 | 𝜔 𝑣𝑣 ⟩ | 𝐷 𝑣𝑣 ⟩ Time dilation: 𝐷 𝑒𝑒𝑒𝑒 𝐷 𝑣𝑣 2 Drop in interference visibility! Experimental implications: Matter wave interferometry with additional internal clock-states | 𝐷⟩  (e.g. | 𝐷⟩ = | 𝑛⟩ + | 𝑓⟩ ) (M. Zych, F. Costa, I. Pikovski , Č. Brukner. Nature comm. 2, 505 (2011)) Shapiro delay: Photons slowed down by gravity  (M. Zych, F. Costa, I. Pikovski , T.C. Ralph, Č. Brukner. Time dilation Class. Quant. Grav. 29, 224010 (2012)) decoherence

Arbitrary composite system in Earth‘s gravitational field. 𝑛 Simple model: Particle has N internal harmonic oscillators: 𝑂 𝐼 0 = � 𝑒 𝑗 ℏ𝜕 𝑗 𝑗=1 Each constituent in equilibrium at temperature T: 𝑒 ⁄ − 1) −1 � 𝑗 = ( 𝑓 ℏ𝜕 𝑗 𝑙 𝐶 𝑈 𝜍 𝑗 = 1 ⁄ | 𝛽 𝑗 ⟩⟨𝛽 𝑗 | � 𝑒 2 𝛽 𝑗 𝑓 − 𝛽 𝑗 2 𝑗 � 𝑗 𝜌𝑒 � 𝑗 GR time dilation induces interaction 𝑂 𝐼 𝑗𝑗𝑗 = 𝑛𝑛𝑛 + ℏ𝑛𝑛 with center-of-mass position x : 𝑑 2 � 𝑒 𝑗 𝜕 𝑗 𝑗=1 Time dilation decoherence

Spatial superposition, internal temperature T : | 𝜔 𝑒𝑑 ⟩ = 1 2 | 𝑛 1 ⟩ + | 𝑛 2 ⟩ , Δ𝑛 𝑂 𝜍 0 = | 𝜔 𝑒𝑑 ⟩⟨𝜔 𝑒𝑑 | ⊗ ∏ 𝜍 𝑗 𝑗=1 𝑕𝑦 Evovles under 𝐼 = 𝑛𝑛𝑛 + (1 + 𝑂 𝑒 2 ) ∑ ℏ𝑒 𝑗 𝜕 𝑗 𝑗=1 Quantum coherence of center-of- mass reduces due to time-dilation: ℏ𝑑 2 2 𝑂 𝑙 𝐶 𝑈𝑛Δ𝑛 ⁄ 𝜖 𝑒𝑠𝑒 = � −𝑂 2 2 𝑗 1 + 𝑙 𝐶 𝑈𝑛Δ𝑛 𝑛 − 𝜐 𝑒𝑒𝑒 𝑊 𝑛 ≈ ≈ 𝑓 ℏ𝑑 2  Universal for all composite systems  Gaussian decay of quantum coherence (for t ≪ 𝑂𝜖 𝑒𝑠𝑒 )  Decoherence mediated by time dilation, depends on internal composition  Relativistic, thermodynamic and quantum mechanical effect  Regular quantum theory and general relativity Time dilation decoherence

Include full dynamics of center-of mass in Born approximation: 2 𝑗 𝜍̇ 𝑒𝑑 𝑛 = − 𝑗 ℏ 𝐼 𝑒𝑑 + 𝐼 0 − Δ𝐼 0 𝑠 𝑑 2 Γ ( 𝑛 , 𝑣 ), 𝜍 𝑒𝑑 𝑛 � 𝑒𝑒 Γ ( 𝑛 , 𝑣 ), Γ ( 𝑛 , 𝑣 ), 𝜍 𝑒𝑑 𝑛 − 𝑒 � ℏ𝑑 2 0 𝑞 2 and where: 𝑠 = 𝑓 −𝑗𝑠𝐼 𝑒𝑑 / ℏ Γ , 𝜍 𝑓 𝑗𝑠𝐼 𝑒𝑑 / ℏ 2𝑑 2 Γ 𝑛 , 𝑣 = 𝑛𝑛 − Γ , 𝜍 � Master equation with only gravitational interaction after build-up of superosition: 2 𝜍̇ 𝑒𝑑 𝑛 = − 𝑗 ℏ 𝐼 𝑒𝑑 + 𝑛 + 𝑂𝑙 𝐶 𝑈 − 𝑂𝑛 𝑙 𝐶 𝑈𝑛 𝑛𝑛 , 𝜍 𝑒𝑑 𝑛 𝑛 , 𝑛 , 𝜍 𝑒𝑑 𝑛 𝑑 2 ℏ𝑑 2 Unitary part. „A piece of iron weighs Decoherence into more when red-hot than when cool“ position basis 2 𝑗 − Off-diagonal elements supressed: 𝜐 𝑒𝑒𝑒 𝑛 1 𝜍 𝑒𝑑 ( 𝑛 ) 𝑛 2 ~ 𝜍 𝑒𝑑 0 𝑓  No „external“ environment  No dissipation ℏ𝑑 2 2  Position pointer-basis  Gaussian decay 𝑙 𝐶 𝑈𝑛Δ𝑛 𝜖 𝑒𝑠𝑒 = 𝑂  No hidden assumptions, Time dilation relies only on time dilation decoherence

μ m-scale object on Earth at room ℏ𝑑 2 2 𝑙 𝐶 𝑈𝑛Δ𝑛 𝜖 𝑒𝑠𝑒 = 10 −3 s temperature, Δx= 10 −6 m : 𝜖 𝑒𝑠𝑒 = 𝑂  Despite small redshift, decoherence is substantial.  Fundamental limit for spatial superpositions on Earth.  Decoherence universally present on curved space-time.  For strong gravitational fields / high accelerations: Very strong decoherence Other decoherence sources also present. Main competing mechanism black- body radiation: 6 10 −3 𝜖 𝑠𝑑 ~ 𝐽𝑛 𝜁 + 2 ℏ𝑑 𝑑𝑠 3 Δ𝑛 2 𝜁 − 1 𝑙 𝐶 𝑈 Green region: decoherence due to time Time dilation dilation dominates over BB-emission. decoherence

 Gravitational effect in quantum theory  General relativistic time dilation leads to entanglement between position and internal degrees-of-freedom  Quantum Hamiltonian can be probed with matter waves with clock-states or with photons via Shapiro delay  Time dilation leads to decoherence of all composite particles, ℏ𝑒 2 2 timescale: 𝜖 𝑒𝑠𝑒 = 𝑙 𝐶 𝑈𝑕Δ𝑦 𝑂  No breakdown of quantum mechanics, as opposed to collapse-theories  Time dilation on Earth decoheres mesoscopic systems  Could be verified in future experiments with molecules or trapped nanospheres I. Pikovski, M. Zych , F. Costa, Č. Brukner. Univ ivers rsal l Decphe herenc nce du due t to Gra Gravit itational T l Tim ime Time dilation Dilatio Dila ion. . ArXiv:1311.1095 (2013). decoherence

Can quantum gravity have signatures in low-energy quantum mechanics? Novel effects seem inevitable at some scale. Modification of Heisenberg uncertainty relation, common to many approaches to QGR: (L. Garay, Int. J. Mod. Phys. A10, 145 (1995)) Usual quantum Δ𝑞 2 Δ𝑛 Δ𝑣 ≥ ℏ 2 (1 + 𝛾 0 2 c 2 ) experiments 𝑁 𝑄𝑄 Current experimental standard QM response of the space-time, bound from quantum M Pl ≈ 22 𝜈𝑛 Planck-mass, systems : 𝛾 0 < 10 33 𝛾 0 dimensionless parameter (S. Das & E. C. Vagenas, PRL 101, 221301 (2008)) Probing Planck- scale physics

A. Kempf, M. Maggiore: Δ𝑛 Δ𝑣 ≥ ℏ 2 (1 + 𝛾Δ𝑣 2 + ⋯ ) implies a modified commutator. E.g.: 2 𝑄 � 2 𝑞 0 � , 𝑄 � 𝛾 = i(1+ 𝛾 0 2 𝑒 2 + ⋯ ) 𝑌 (A. Kempf, G. Mangano and R. Mann,  𝑁 𝑄𝑄 PRD, 52, 2 (1995)) � / 𝑒 2 +𝑑 2 𝑞 0 𝑄 � , 𝑄 � 𝜈 = i 1 + 2 𝜈 0 + ⋯ (M. Maggiore, Phys. Lett. B, 319 (1993)) 𝑌  2 𝑁 𝑄𝑄 2 𝑄 � 2 � 𝑁 𝑄𝑄 𝑒 + 𝛿 02 𝑞 0 𝑞 0 𝑄 2 𝑒 2 + ⋯ ) (A. F. Ali, S. Das and E. C. Vagenas, � , 𝑄 � 𝛿 = i(1 − 𝛿 0 𝑌  Phys. Lett. B, 678 (2009) 𝑁 𝑄𝑄 Examples: 2 → 𝑣 0 ω / 2𝜌 = 10 kHz, 2 𝑑 2 ~ 10 −60 very small Ions in harmonic trap: 𝑛 = 10 −27 kg 𝑁 𝑄𝑄 2 → 𝑣 0 Optomechanics: ω / 2𝜌 = 100 MHz, 2 𝑑 2 ~ 10 −40 𝑁 𝑄𝑄 𝑛 = 10 −12 kg Probing Planck- scale physics