Can we show that cosmological structures are of quantum mechanical origin?

Transcription

1 Can we show that cosmological structures are of quantum mechanical origin? Vincent Vennin COSMO Conference, Paris, 31 st

2 Outline Based on - J MarFn and VV 2015, arxiv: (PRD) - J MarFn and VV 2016, arxiv: (PRA) - J MarFn and VV 2016, arxiv: (PRA) - J MarFn and VV 2017, arxiv: (PRD) Do primordial density fluctuafons contain quantum correlafons? Can we violate Bell inequalifes? Can we exclude a purely classical explanafon? 0/10

3 Cosmological Perturbations in In5lation InflaFon is a high energy phase of accelerated expansion in the early Universe ds2 = dt2 + a2 (t) d~x2 with a > 0 Quantum vacuum fluctuaFons are stretched to cosmological scales k wavelength ParFcle ProducFon à a/a Hubble radius Fme Quantum Mechanics on Cosmological Scales! CMB à Minkowski vacuum Structure FormaFon Can we test it? 1/10

4 A B Quantum Discord Henderson and Vedral 2001, Ollivier and Zurek 2001 Adesso, Bromley, Cianciaruso 2016 Idea: Find two ways to calculate the mutual informaeon between A and B that coincide for classical correlaeons but may differ in quantum systems I = S(A)+S(B) S(A, B) 2/10

5 A B Quantum Discord Henderson and Vedral 2001, Ollivier and Zurek 2001 Adesso, Bromley, Cianciaruso 2016 Idea: Find two ways to calculate the mutual informaeon between A and B that coincide for classical correlaeons but may differ in quantum systems I = S(A)+S(B) S(A, B) J = S(A) S(A B) 2/10

6 A B Quantum Discord Henderson and Vedral 2001, Ollivier and Zurek 2001 Adesso, Bromley, Cianciaruso 2016 Idea: Find two ways to calculate the mutual informaeon between A and B that coincide for classical correlaeons but may differ in quantum systems I = S(A)+S(B) S(A, B) J = S(A) S(A B) ˆ j : complete set of projectors defined on E B ˆ! ˆ ˆ j /p j with probability p j =Tr ˆ ˆ j S(A B) = X p j S A; ˆ j j and A; ˆ j =Tr B ˆ j /p j 2/10

7 A B Quantum Discord Henderson and Vedral 2001, Ollivier and Zurek 2001 Adesso, Bromley, Cianciaruso 2016 Idea: Find two ways to calculate the mutual informaeon between A and B that coincide for classical correlaeons but may differ in quantum systems I = S(A)+S(B) S(A, B) J = S(A) S(A B) with respect to measurements ˆ j (A, B) =min { ˆ j } (I J ) 2/10

8 Quantum Discord of Cosmic In5lation One scalar degree of freedom: v / (curvature perturbafon) / T/T (CMB T fluctuafon) 1 i = O ki with ki = coshr k2r 3+ k Two-mode squeezed state (Gaussian state) 1X e 2in' k ( n= ) n tanh n r k n k,n k i (k, k) = cosh 2 r k log 2 cosh 2 r k 2.0 sinh 2 r k log 2 sinh 2 r k 150 at the end of inflafon Large degree of quantum correla;ons! Can we design a Bell-type experiment? δ (k, k) ln 2 r k r k 3/10

9 Bell Experiments in the CMB Spin operators for confnuous variables (Larsson 2004) 1X Z (n+1)` Ŝ z (`) = ( 1) n dq QihQ n= 1 Ŝ x (`) =Ŝ+(`)+Ŝ +(`) i Ŝ y (`) = i hŝ+ with Ŝ + (`) = (`) Ŝ +(`) n` 1X Z (2n+1)` ( 1) n n= 1 2n` dq QihQ + ` ˆB ϕ π/ ϕ =0.34 e r ˆB max r =3, ϕ =0 r =3, ϕ =0.01 r =3, ϕ = log 2 l r =3, ϕ =0.02 r =3, ϕ = r /10

10 Bell Experiments in the CMB Spin operators for confnuous variables (Larsson 2004) 1X Z (n+1)` Ŝ z (`) = ( 1) n dq QihQ n= 1 Ŝ x (`) =Ŝ+(`)+Ŝ +(`) i Ŝ y (`) = i hŝ+ with Ŝ + (`) = (`) Ŝ +(`) n` 1X Z (2n+1)` ( 1) n n= 1 2n` dq QihQ + ` How do we measure the spin operators? T/T! k! v k, find n such that n` apple v k < (n + 1)` and S z =( 1) n posieon measurement only Ŝ x and Ŝ y require to measure the conjugated momentum k 0 e r k k, which may be concealed from us for ever See also Campo and Parentani 2005 Maldacena 2014 Can we detect quantum correla;ons using posi;on measurements only? 5/10

11 Legget-Garg Experiments in the CMB E Two-Fme correlators C ab = DŜz (t a, `)Ŝz(t b, `) Legget-Garg three-strings: K 3 = C ab + C bc C ac, K 0 3 = C ab C bc C ac Classically 3 apple K 3,K 0 3 apple 1 temporal Bell inequalifes 6/10

12 Legget-Garg Experiments in the CMB 7/10

13 Legget-Garg Experiments in the CMB E Two-Fme correlators C ab = DŜz (t a, `)Ŝz(t b, `) Legget-Garg three-strings: K 3 = C ab + C bc C ac, K 0 3 = C ab C bc C ac Classically 3 apple K 3,K 0 3 apple 1 temporal Bell inequalifes But requires to measure at three different Fmes Can we detect quantum correla;ons using single-;me, posi;on measurements only? 8/10

14 Back to Discord: Classical States Classical states non-discordant states (δ=0) Can we exclude non-discordant states? Theorem: the only classical Gaussian states are product states (Adesso and DaVa 2010; Rahimi-Keshari, Caves, Ralph 2013; Mista, McNulty, Adesso 2014) I =0,nG=0) I =0 CMB must be quantum? can be classical ng = S( G ) S( ) 9/10

15 Conclusions Cosmological perturba;ons are placed in a two-mode highly squeezed state in the very early Universe Such a state has a large quantum discord, denofng the presence of large quantum correla;ons between parfcles created with opposite wave momenta In principle, Bell experiments can therefore be constructed that would prove that CMB anisotropies are of quantum mechanical origin In pracfce, these experiments require to measure exponenfally small quanffes ( decaying mode), at least in the standard setup Legget-Garg inequalifes evade this issue but require to measure perturbafons at different ;mes The CMB cannot have been placed in a classical Gaussian state. Current constraints on non-gaussianifes may be already sufficient to exclude non-discordant states! 10/10