Experimental Quantum Cosmology: Probing Analogue TransPlanckian Physics in Dipolar Bose-Einstein Condensates

Uwe R. Fischer Seoul National University Group: Theory of Cold Atoms

July 23, 2019, Trento

Uwe R. Fischer Experimental Quantum Cosmology Probing the Transplanckian World with Analogue Gravity

Analogue “Gravity” ≡

Fundamental Kinematical Effects [Visser, PRL 80 (1998)] For Quantum Fields Propagating In Curved Spacetime (Spacetime Fixed by Experimentalist!)

In Particular: I. Extreme Spacetime Curvatures II. Impact of Transplanckian Physics Can be Investigated in Analogue Experiments

Uwe R. Fischer Experimental Quantum Cosmology I Gibbons-Hawking Effect (Unruh Effect in de Sitter Universe) [Fedichev & URF, PRL 91 (2003)]

I Cosmological Particle Production, Sakharov Oscillations [Barcel´oet al, PRA 68 (2003); Fedichev & URF, PRA 69 (2004) Jaskula et al, PRL 109 (2012); Hung et al, Science 341 (2013)]

I Universe Inflation and Mode Freezing [URF & Sch¨utzhold,PRA 70 (2004); Eckel et al, PRX 8 (2018)]

Examples for Kinematical (≡ non-Einstein Equation) Effects in BECs

I Hawking Radiation [Garay et al, PRL 85 (2000); Barcel´oet al, IJMPB 18 (2003) Carusotto et al, NJP 10 (2008); de Nova et al, Nature 569 (2019)]

Uwe R. Fischer Experimental Quantum Cosmology I Cosmological Particle Production, Sakharov Oscillations [Barcel´oet al, PRA 68 (2003); Fedichev & URF, PRA 69 (2004) Jaskula et al, PRL 109 (2012); Hung et al, Science 341 (2013)]

I Universe Inflation and Mode Freezing [URF & Sch¨utzhold,PRA 70 (2004); Eckel et al, PRX 8 (2018)]

Examples for Kinematical (≡ non-Einstein Equation) Effects in BECs

I Hawking Radiation [Garay et al, PRL 85 (2000); Barcel´oet al, IJMPB 18 (2003) Carusotto et al, NJP 10 (2008); de Nova et al, Nature 569 (2019)]

I Gibbons-Hawking Effect (Unruh Effect in de Sitter Universe) [Fedichev & URF, PRL 91 (2003)]

Uwe R. Fischer Experimental Quantum Cosmology I Universe Inflation and Mode Freezing [URF & Sch¨utzhold,PRA 70 (2004); Eckel et al, PRX 8 (2018)]

Examples for Kinematical (≡ non-Einstein Equation) Effects in BECs

I Hawking Radiation [Garay et al, PRL 85 (2000); Barcel´oet al, IJMPB 18 (2003) Carusotto et al, NJP 10 (2008); de Nova et al, Nature 569 (2019)]

I Gibbons-Hawking Effect (Unruh Effect in de Sitter Universe) [Fedichev & URF, PRL 91 (2003)]

I Cosmological Particle Production, Sakharov Oscillations [Barcel´oet al, PRA 68 (2003); Fedichev & URF, PRA 69 (2004) Jaskula et al, PRL 109 (2012); Hung et al, Science 341 (2013)]

Uwe R. Fischer Experimental Quantum Cosmology Examples for Kinematical (≡ non-Einstein Equation) Effects in BECs

I Hawking Radiation [Garay et al, PRL 85 (2000); Barcel´oet al, IJMPB 18 (2003) Carusotto et al, NJP 10 (2008); de Nova et al, Nature 569 (2019)]

I Gibbons-Hawking Effect (Unruh Effect in de Sitter Universe) [Fedichev & URF, PRL 91 (2003)]

I Cosmological Particle Production, Sakharov Oscillations [Barcel´oet al, PRA 68 (2003); Fedichev & URF, PRA 69 (2004) Jaskula et al, PRL 109 (2012); Hung et al, Science 341 (2013)]

I Universe Inflation and Mode Freezing [URF & Sch¨utzhold,PRA 70 (2004); Eckel et al, PRX 8 (2018)]

Uwe R. Fischer Experimental Quantum Cosmology I. Cosmological Particle Production (CPP)

Time Dependent Variation of Spacetime Metric in Expanding Cosmos OR Time Dependence of Boundary Conditions in Cavity (Dynamical Casimir Effect)

CPP Concept: Schr¨odinger,Physica 6 (1939) “The proper vibrations of the expanding universe”

QFT Elaboration of CPP: Parker, PRL 21 (1968)

Dynamical Casimir: Moore, J Math Phys 11 (1970)

CPP aka Dynamical Casimir (aka Parametric Downconversion in Quantum Optics)

Uwe R. Fischer Experimental Quantum Cosmology Dynamical Casimir or CPP in BECs

Simple Recipe: Do Something Explicitly Time-Dependent to System

For Example:

(a) Coupling Constant(s) gc (t) [Feshbach Resonance]

(b) Trapping Vtrap = Vtrap(t)

[ωtrap = ωtrap(t) or Split into Double Well]

=⇒ CPP Generic Effect of Mode Mixing (Conversion of Positive to Negative Frequency Modes)

Uwe R. Fischer Experimental Quantum Cosmology II. Scale Invariance of Cosmological Power Spectrum

Cosmological Density Perturbations (≡ Inflaton) in

Inflationary Quantum Cosmology Guth, PRD 23 (1981); Linde, PLB 108 (1982)

Inflaton Mode Freezing After Crossing of Cosmological Horizon

Standard Quantum Mechanism for Galaxy Formation: Formation of Inhomogeneities in Initially Homogeneous Universe

Mukhanov, Physical Foundations of Cosmology (CUP 2005)

Uwe R. Fischer Experimental Quantum Cosmology Chapter 1 of Transplanckian Analogue Simulation:

Inflation and Scale Invariance of Power Spectrum

Exponential De Sitter Evolution of Cosmological Scale Factor √ a(τ) = exp[Hτ] H ∝ Λ ≡ Hubble Constant

Consider Power Spectrum of Phase-Phase (Inflaton) Correlator 1 X h0|δφˆ(x, τ)δφˆ(y, τ)|0i := P(k)eik·(x−y) V k ~H −2 Late Cosmological Times τ: P(k) → 2 k πmc0 Definition of Scale Invariance:

∆2(k) := k2P(k) Independent of k

Hallmark Signature of Inflationary Quantum Cosmology

Note: Use D=2 Variant Here [P(k) ∝ k−D ]

Uwe R. Fischer Experimental Quantum Cosmology Trans-Planckian Problem of Inflationary Cosmology

Comoving Wavelengths λ ∼ O(λPL) Probe Planck Scale During Early Cosmological Stages

Scale Invariance Broken by Trans-Planckian Effects??

“Trans-Planckian Problem of Inflationary Cosmology”

Martin & Brandenberger, PRD 63 (2001)

Problem: Dispersion Relation Not Known for “Real” Gravity No Quantum Gravity Exists!

=⇒ Take Analog Model with Well-Known Microscopics:

Condensed Matter Physics Comes to the Rescue... Volovik, “The Universe in a Helium Droplet”, Oxford UP

Uwe R. Fischer Experimental Quantum Cosmology Dipolar Bose-Einstein Condensate

3g 1 − 3z2/|r|2 V (r) = d g ∝ µ2 dd 4π |r|3 d m,e

Pancake With ⊥-Polarized Dipoles For Stability

Large Magnetic Dipole Moment µm: Cr, Dy, Er (Tune in Addition Contact Coupling with Feshbach...)

Pfau (Stuttgart), Lev (Stanford), Ferlaino (Innsbruck) Modugno (Firenze, Pisa) [more to come...]

Electrically Dipolar BEC: Ongoing Work in Progress Uwe R. Fischer Experimental Quantum Cosmology (Quasi-2D) Bogoliubov Excitations

ζ = kdz 2  √  4 ε 2 3R 2 ζ 2 = Aζ 1 − ζ exp[ζ /2] erfc[ζ/ 2] + (~ωz,0) 2 4

2 A ∝ ρ0dz gd /R Chemical Potential

p −1 p R = π/2(1 + gc /2gd ) ' π/2 Coupling Ratio

URF, PRA Rapids 73 (2006)

Uwe R. Fischer Experimental Quantum Cosmology Definition of “Trans-Planckian” Physics

Beyond Linear (Sound) Part: Physics not (Pseudo-)Lorentz Invariant

Large Dipolar Coupling (R → pπ/2): Curvature Negative

Dispersion Develops “Roton” Minimum

Impact of High-Momentum, Low-Energy Quasi-Particles On (small-k) Quantum Fields in Curved Spacetime?

Question Here: Scale Invariance Maintained?

Uwe R. Fischer Experimental Quantum Cosmology Scaling Expansion of Dipolar BEC

Scaling Ansatz [Kagan et al., Castin & Dum (1996); Gritsev et al (2010)] Z t 0  2  r dt mr ∂t b ψ(x, τ) x := τ := 2 0 Ψ(r, t) := exp i b(t) 0 b (t ) 2~ b b

3 2 4 2 b ∂t b + b ω (t) gc (t) gd (t) provided 2 = = ω0 gc,0b gd,0b

Exact Solution for Constant gc , gd : (Slow) Square Root Expansion √ 2 2 5 2 4 b(t) = 4Ht + 1, ω (t) = ω0/b + 4H /b

Robertson-Walker (a) and BEC (b) Universes Have

Scale Factor Relation a2 = b (Contact Interaction: a = b)

Uwe R. Fischer Experimental Quantum Cosmology Time-Dependent Bogoliubov Mode Functions √ Analytical Solution when b(t) = 4Ht + 1 s π VH h i δφ˜ (s) = s ~ J (s) + iY (s) := h (s) k 2 2 1 1 k 4mc0 k Initial Free Oscillation =⇒ Overdamped for Large s c /H Hubble radius s(t) = 0 ≡ a(t)/k rescaled wavelength

Modes hk (s) Correspond to Instantaneous Bunch-Davies Vacuum [Chernikov & Tagirov; Schomblond & Spindel, Ann Inst H Poincar´e IX & XXV (1968 & 1976); Bunch & Davies, Proc Roy Soc A 360 (1978)]

“BD Vacuum” ≡ (Quasi-)Particle-Vacuum Free-Falling Observer ⇒ Yields in (Formally) Infinite Past BEC Quasi-Particle Vacuum in Minkowski Space

Uwe R. Fischer Experimental Quantum Cosmology Horizon Crossing and Mode Freezing In Conformal Time: ds2 = a2[dη2 − dx2]

(a) relativistic limit (b) ζ = 0.0005 )

k 5 5 ˜ φ δ

k 0 0 (

ℑ -5 -5 −

-102 -100 -100

(c) ζ = 0.04 (d) ζ = 0.1 )

k 5 5 ˜ φ δ

k 0 0 (

ℑ -5 -5 −

-100 -102 -100 kη kη “Galaxy Formation” in Analogue Inflationary Quantum Cosmology ⇐⇒ Bogoliubov Modes Get “Frozen In”

Uwe R. Fischer Experimental Quantum Cosmology Violation of Scale Invariance?

Microscopic Excitation Spectrum During Expansion

(a) 2.5 (b)

2 6 1.5 4

2 1 ε ε 4

a 2 0.5

0 0 e1 -0.5 2 e0.5 0 0.5 1 1.5 2 2.5 1 a aζ 1 0 ζ

Expansion: Gas Becomes More Dilute

However: Initial “Roton” Minimum Leaves Imprint

On Power Spectrum of Phase-Phase Correlations

=⇒ Window on Transplanckian Physics In Early (Analogue) Universe!

Uwe R. Fischer Experimental Quantum Cosmology Phase-Phase Correlations in Fourier Space: Power Spectrum 2.2 scale invariance 2 R = 0 A = Ac/10 1.8 A = Amin A = Ac A = 1.1A ) 1.6 c k ( 2

∆ 1.4

1.2

1

0.8 0 0.02 0.04 0.06 0.08 0.1 ζ Significant Violations of Scale Invariance For Almost Critical (Initial) Spectrum Roton Minimum Imprint! Adiabaticity of Mode Propagation Violated for Deep Minimum Ch¨a& URF, PRL 118, 130404 (2017)

Uwe R. Fischer Experimental Quantum Cosmology Chapter 2 of Transplanckian Analogue Simulation:

Roton Entanglement and Steering in Quenched Condensates

Dynamical Casimir Effect (aka Cosmological Particle Production) Here: Created by Quench of Sound Speed

=⇒ Pairs of Quasiparticles Created with Momenta k and −k

Enhanced Production Near Roton Minimum (Heisenberg Helps...)

Quasiparticle Pairs Entangled/Steered?

Dilute Gas: Tractable with Time-Dependent Bogoliubov Theory

Uwe R. Fischer Experimental Quantum Cosmology Entanglement and Steering Primer

Entanglement ≡ Nonseparability of Quantum States Entanglement: Schr¨odinger, Naturwissenschaften 23 (1935)

Steerable States ≡ Subset of Nonseparable States Steering: Schr¨odinger, Math Proc Cambr Phil Soc 31 (1935)

Bipartite Steerable States Have “Half” of Bell-Nonlocality:

Alice Performs Uncharacterized Measurements Not Accessible (Hidden) to Bob

=⇒ Inferred Standard Dev of Noncommuting A, B Observables Can Violate Standard Heisenberg Uncertainty Relation

Steerable Quantum States (a) Subset of Entangled States (b) Superset of Bell States

Uwe R. Fischer Experimental Quantum Cosmology Entanglement and Steering Criteria for CV Systems

Density Fluctuation Operator

δρˆk(τ) † = (uk + vk)(ϕ ˆk(τ) +ϕ ˆ−k(τ)) ρ0

uk, vk Bogoliubov Transformation Amplitudes

ϕˆk Quasiparticle Field Operators Density-Density Correlation Function

h|δρˆ (τ)|2i k 2 −2iωkτ G2,k(τ) = 2 = (uk + vk) (2nk + 1 + 2<[cke ]) ρ0

ˆ† ˆ nk = hbkbki Mean Quasiparticle Occupation Number

ck = hbˆkbˆ−ki Quasiparticle Pair Amplitude

Uwe R. Fischer Experimental Quantum Cosmology Assessing Entanglement and Steering

Density-Density Correlations: Experimentally Accessible Measure of Quasiparticle Entanglement

Robertson, Michel, Busch & Parentani PRA 89 (2014), PRD 95 & 96 (2017) Finazzi & Carusotto, PRA 90 (2014)

vac 2 G2,k(τ) < G2,k = (uk + vk) [Nonseparable] 1 G (τ) < G vac [Steerable, More Strict Criterion!] 2,k 2 2,k

=⇒ Vacuum Amplitude of Density-Density Correlations Decides On Entanglement and Steering

Uwe R. Fischer Experimental Quantum Cosmology Stationary Density-Density Correlations

5

R 0 4 = 2 A=Ac10 Ωk@units of mc0D

A=Amin=1.249 2.5 3 R=0 A A 10

k A 3.1 = c = 2.0 A A 1.249 2, = min= A=Ac=3.4454 A 3.1 G 1.5 = 2 A=Ac=3.4454 1.0

1 0.5

kΞ 0.0 0.5 1.0 1.5 2.0 0 0 0 1 2 3 4

kΞ0

Correlation Peak at Roton Minimum Contact Interactions: No Peak

Uwe R. Fischer Experimental Quantum Cosmology Quench of Sound Speed

Scale Factor b(t) of Gas in Lab Time

1.0 a=0.2 0.9 a=0.5 0.8 a=1 L t H b 0.7

0.6

0.5 0 10 20 30 40 t @arb. unitsD

=⇒ Gas Contraction

Uwe R. Fischer Experimental Quantum Cosmology Roton-Enhanced Entanglement and Steering ˜ vac Normalized Correlations G2,k := G2,k/G2,k Ž G2, kHΤmL 2.0 2 Ωk@units of mc0D

2.5 1.5 R=0 A=Ac10 2.0 A=Amin=1.249 1.5 A=3.1 1.0 A=Ac=3.4454 1.0

nonseparable 0.5 0.5 kΞ steerable 0.0 0.5 1.0 1.5 2.0 0

kΞ f 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Increasing Roton Depth ⇒ Increased Entanglement Potential

Uwe R. Fischer Experimental Quantum Cosmology Visualization with Envelopes and T 6= 0 Ž Ž G2, kHΤmL G2, kHΤmL 2.0 2.0

1.5 1.5

1.0 1.0 nonseparable nonseparable 0.5 0.5 steerable steerable

kΞ f kΞ f 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

2 Temperature T = 0 T = mc0 Black: Solely Contact Interactions Purple: Critical Dipole-Dipole Interaction Dominated Gas =⇒ Roton Minimum Generally Strongly Enhances Entanglement and Steering

Tian, Ch¨a& URF, Phys. Rev. A 97, 063611 (2018)

Uwe R. Fischer Experimental Quantum Cosmology I Violations of Scale Invariance Observable: First Such Analogue Gravity System! More Typically: No Violations [cf Niemeyer and Parentani, PRD 64 (2001)]

I However: Even With “Roton Minimum” Exact Scale Invariance Possible! Details of Transplanckian Dispersion Matter Ch¨a& URF, PRL 118, 130404 (2017) [in Supplement]

I Strong Quantum Fluctuations of Electric-Dipole BEC: Possible Influence on Early (Pre-Metric?) Stage of Cosmological Evolution

Summary Chapter 1 of Analogue TransPlanckian Simulation

I Trans-Planckian Problem of Inflationary Cosmology Experimentally Accessible in Dipolar BEC

Uwe R. Fischer Experimental Quantum Cosmology I However: Even With “Roton Minimum” Exact Scale Invariance Possible! Details of Transplanckian Dispersion Matter Ch¨a& URF, PRL 118, 130404 (2017) [in Supplement]

I Strong Quantum Fluctuations of Electric-Dipole BEC: Possible Influence on Early (Pre-Metric?) Stage of Cosmological Evolution

Summary Chapter 1 of Analogue TransPlanckian Simulation

I Trans-Planckian Problem of Inflationary Cosmology Experimentally Accessible in Dipolar BEC

I Violations of Scale Invariance Observable: First Such Analogue Gravity System! More Typically: No Violations [cf Niemeyer and Parentani, PRD 64 (2001)]

Uwe R. Fischer Experimental Quantum Cosmology I Strong Quantum Fluctuations of Electric-Dipole BEC: Possible Influence on Early (Pre-Metric?) Stage of Cosmological Evolution

Summary Chapter 1 of Analogue TransPlanckian Simulation

I Trans-Planckian Problem of Inflationary Cosmology Experimentally Accessible in Dipolar BEC

I Violations of Scale Invariance Observable: First Such Analogue Gravity System! More Typically: No Violations [cf Niemeyer and Parentani, PRD 64 (2001)]

I However: Even With “Roton Minimum” Exact Scale Invariance Possible! Details of Transplanckian Dispersion Matter Ch¨a& URF, PRL 118, 130404 (2017) [in Supplement]

Uwe R. Fischer Experimental Quantum Cosmology Summary Chapter 1 of Analogue TransPlanckian Simulation

I Trans-Planckian Problem of Inflationary Cosmology Experimentally Accessible in Dipolar BEC

I Violations of Scale Invariance Observable: First Such Analogue Gravity System! More Typically: No Violations [cf Niemeyer and Parentani, PRD 64 (2001)]

I However: Even With “Roton Minimum” Exact Scale Invariance Possible! Details of Transplanckian Dispersion Matter Ch¨a& URF, PRL 118, 130404 (2017) [in Supplement]

I Strong Quantum Fluctuations of Electric-Dipole BEC: Possible Influence on Early (Pre-Metric?) Stage of Cosmological Evolution

Uwe R. Fischer Experimental Quantum Cosmology I Creates Entanglement and Steering of Rotonic Quasiparticle Excitations

I Dipolar Gas: Enhanced Potential for Nonlocal Quantum Correlations Tian, Ch¨a& URF, Phys. Rev. A 97, 063611 (2018)

I Ad: Analogue Gravity Postdoc Positions Available! Reversing Rutherford: “When a young man in my lab uses the word Universe, I tell him it is time for him to leave”

Chapter 2 in Analogue TransPlanckian Simulation

I Dynamical Casimir Effect of Quenched Dipolar Gas

Uwe R. Fischer Experimental Quantum Cosmology I Dipolar Gas: Enhanced Potential for Nonlocal Quantum Correlations Tian, Ch¨a& URF, Phys. Rev. A 97, 063611 (2018)

I Ad: Analogue Gravity Postdoc Positions Available! Reversing Rutherford: “When a young man in my lab uses the word Universe, I tell him it is time for him to leave”

Chapter 2 in Analogue TransPlanckian Simulation

I Dynamical Casimir Effect of Quenched Dipolar Gas

I Creates Entanglement and Steering of Rotonic Quasiparticle Excitations

Uwe R. Fischer Experimental Quantum Cosmology I Ad: Analogue Gravity Postdoc Positions Available! Reversing Rutherford: “When a young man in my lab uses the word Universe, I tell him it is time for him to leave”

Chapter 2 in Analogue TransPlanckian Simulation

I Dynamical Casimir Effect of Quenched Dipolar Gas

I Creates Entanglement and Steering of Rotonic Quasiparticle Excitations

I Dipolar Gas: Enhanced Potential for Nonlocal Quantum Correlations Tian, Ch¨a& URF, Phys. Rev. A 97, 063611 (2018)

Uwe R. Fischer Experimental Quantum Cosmology Chapter 2 in Analogue TransPlanckian Simulation

I Dynamical Casimir Effect of Quenched Dipolar Gas

I Creates Entanglement and Steering of Rotonic Quasiparticle Excitations

I Dipolar Gas: Enhanced Potential for Nonlocal Quantum Correlations Tian, Ch¨a& URF, Phys. Rev. A 97, 063611 (2018)

I Ad: Analogue Gravity Postdoc Positions Available! Reversing Rutherford: “When a young man in my lab uses the word Universe, I tell him it is time for him to leave”

Uwe R. Fischer Experimental Quantum Cosmology “I’m traveling at the speed of light I wanna make a supersonic man out of you”

So: Don’t Stop Analogue Gravity Now!

Queen’s Prophecy

Don’t stop me now (1978):

Uwe R. Fischer Experimental Quantum Cosmology I wanna make a supersonic man out of you”

So: Don’t Stop Analogue Gravity Now!

Queen’s Prophecy

Don’t stop me now (1978):

“I’m traveling at the speed of light

Uwe R. Fischer Experimental Quantum Cosmology So: Don’t Stop Analogue Gravity Now!

Queen’s Prophecy

Don’t stop me now (1978):

“I’m traveling at the speed of light I wanna make a supersonic man out of you”

Uwe R. Fischer Experimental Quantum Cosmology Queen’s Prophecy

Don’t stop me now (1978):

“I’m traveling at the speed of light I wanna make a supersonic man out of you”

So: Don’t Stop Analogue Gravity Now!

Uwe R. Fischer Experimental Quantum Cosmology