superradiant-like states Mehmet Emre Tasgin Outline Relation - - PowerPoint PPT Presentation

▶
superradiant like states
SMART_READER_LITE
LIVE PREVIEW

superradiant-like states Mehmet Emre Tasgin Outline Relation - - PowerPoint PPT Presentation

Feb 12, 2023 336 likes •681 views

Many-particle entanglement criterion for superradiant-like states Mehmet Emre Tasgin Outline Relation among i. single-mode nonclassicality ii. two-mode entanglement iii. many-particle entanglement new N-particle entanglement

slide-1
SLIDE 1

Mehmet Emre Tasgin

Many-particle entanglement criterion for superradiant-like states

slide-2
SLIDE 2

Outline

  • Relation among

i. single-mode nonclassicality ii. two-mode entanglement iii. many-particle entanglement

  • new N-particle entanglement criterion

i. test for Dicke states ii. test for the ground state Dicke Hamilonian (superradiance) iii. test for single-photon superradiance (exact, time depndt)

  • iv. test for random superposition of Dicke states

v. ground state of an interacting BEC

slide-3
SLIDE 3

3 kind of nonclassicalities

(i) single-mode nonclassicality (ii) two-mode entanglement (iii) many-particle inseperability

slide-4
SLIDE 4

(i) single-mode nonclassicality

(i) single-mode nonclassicality quadrature squeezed states witnessed by photon number squeezed states witnessed by Fock-like (number-like) states works fine for superposition

  • f Fock-states

anti-bunching Mandel Q < 0

slide-5
SLIDE 5

(ii) two-mode entanglement

(ii) two-mode entanglement two-mode squeezed states witnessed by [1-3] DGCZ and SPH inseparable number state witnessed by H&Z criterion [4] works fine for superposition of number-states

[1] Lu-Ming Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000). [2] R. Simon, Phys. Rev. Lett. 84, 2726 (2000). [3] Stefano Mancini, Vittorio Giovannetti, David Vitali, and Paolo Tombesi, Phys. Rev. Lett. 88, 120401 (2002). [4] M. Hillery and M. S. Zubairy, Phys. Rev. Lett. 96, 050503 (2006).

slide-6
SLIDE 6

(iii) many-particle inseparability

(iii) many-particle inspeperability spin-squeezed states witnessed by [7] Dicke states (number-like) superpositions

  • f Dicke states ??
  • eg. superradiant states?

[5] Kitagawa, M. & Ueda, M. Squeezed spin states. Phys. Rev. A 47, 5138 (1993). [6] M. E. Tasgin and P. Meystre, “Spin sqz with coherent light via ent. swapping,” Phys. Rev. A 83, 053848 (2011). [7] A. Sørensen, L.-M. Duan, J. I. Cirac, and P. Zoller, Nature (London) 409, 63 (2001). [8] L-M Duan, “Entanglmnt detection in the vicinity of arbitrary Dicke states,” Phys. Rev. Lett. 107, 180502 (2011).

[5] [6] [7] Duan [8] Duan [8]

𝝄𝒐𝒇𝒙 ? ? ?

slide-7
SLIDE 7

a question in place

[6] M. E. Tasgin and P. Meystre, “Spin sqz with coherent light via ent. swapping,” Phys. Rev. A 83, 053848 (2011).

Atomic coherent states (ACS) separable many-particle states

  • perate

generates many-particle entanglement

  • perate

cannot generate entanglement

  • perate
  • perate

generates two-mode entanglement cannot generate two-mode entanglement

beam-splitter Hmlt

WHY CANNOT ???

(we will answer soon)

slide-8
SLIDE 8

relation:

single-mode noncls. & two-mode entangle.

[9] M. S. Kim, W. Son, V. Buˇzek, and P. L. Knight, “Entanglement by a beam splitter: Nonclassicality as a prerequisite for entanglement,” Phys. Rev. A 65, 032323 (2002).

[9]

beam-splitter (BS) 𝒃𝟐 𝒄𝟐 𝒄𝟑 𝑐1 & 𝑐2 are entangled “only if” 𝑏1is single-mode nonclassical use 𝑐1 & 𝑐2 entanglement criteria single-mode nonclassicality criteria for 𝑏1

  • btain
slide-9
SLIDE 9

relation:

single-mode noncls. & two-mode entangle.

[10] Mark Hillery and M Suhail Zubairy, Phys. Rev. A 74, 032333 (2006). [11] M.E. Tasgin, arXiv:1502.00992v1. [12] M.E. Tasgin , arXiv:1502.00988v1

[9]

beam-splitter (BS) 𝒃𝟐 𝒄𝟐 𝒄𝟑 𝑐1 & 𝑐2 are entangled “only if” 𝑏1is single-mode nonclassicaly DGCZ criterion quadrature squeezing criterion

implies

H&Z criterion number squeezing criterion

implies

slide-10
SLIDE 10

relation:

single-mode noncls. & two-mode entangle.

DGCZ criterion

B.S.

two-mode

quadrature squeezing criterion

single-mode

number sqz criterion

single-mode

H&Z criterion

two-mode

B.S.

[10] Mark Hillery and M Suhail Zubairy, Phys. Rev. A 74, 032333 (2006). [11] M.E. Tasgin, arXiv:1502.00992v1. [12] M.E. Tasgin , arXiv:1502.00988v1

slide-11
SLIDE 11

relation:

single-mode noncls. & many-particle entangl.

[13] JM Radcliffe, “Some properties of coherent spin states,” Journal of Physics A: General Physics 4, 313 (1971). [14] JR Klauder and Bo-Sture Skagerstam, “Applications in physics and mathematical physics,” World Scientific, Singapore (1985).

coherent states

  • f light |𝜷〉

ACS=

separable

𝑶 → ∞ [13,14]

slide-12
SLIDE 12

relation:

single-mode noncls. & many-particle entangl.

[13] JM Radcliffe, “Some properties of coherent spin states,” Journal of Physics A: General Physics 4, 313 (1971). [14] JR Klauder and Bo-Sture Skagerstam, “Applications in physics and mathematical physics,” World Scientific, Singapore (1985).

coherent states

  • f light |𝜷〉

ACS=

separable

𝑶 → ∞ [13,14] 𝑶 → ∞ 𝑶 → ∞

slide-13
SLIDE 13

relation:

single-mode noncls. & many-particle entangl.

[13] JM Radcliffe, “Some properties of coherent spin states,” Journal of Physics A: General Physics 4, 313 (1971). [14] JR Klauder and Bo-Sture Skagerstam, “Applications in physics and mathematical physics,” World Scientific, Singapore (1985).

coherent states

  • f light |𝜷〉

ACS=

separable

𝑶 → ∞ [13,14] 𝑶 → ∞ 𝑶 → ∞

if 𝑠 ≠ 1 ⇒ |𝜔𝑂〉 inseparable if 𝑠 ≠ 1 ⇒ |𝜔〉 single-mode nonclassical

slide-14
SLIDE 14

relation:

single-mode noncls. & many-particle entangl.

[13] JM Radcliffe, “Some properties of coherent spin states,” Journal of Physics A: General Physics 4, 313 (1971). [14] JR Klauder and Bo-Sture Skagerstam, “Applications in physics and mathematical physics,” World Scientific, Singapore (1985).

coherent states

  • f light |𝜷〉

ACS=

separable

𝑶 → ∞ [13,14] 𝑶 → ∞ 𝑶 → ∞

if 𝑠 ≠ 1 ⇒ |𝜔𝑂〉 inseparable if 𝑠 ≠ 1 ⇒ |𝜔〉 single-mode nonclassical |𝜔𝑂〉 inseparable |𝜔〉 single-mode nonclassical

slide-15
SLIDE 15

relation:

single-mode noncls. & many-particle entangl.

[15] Clive Emary and Tobias Brandes, “Chaos and the quantum phase transition in the dicke model,” Phys. Rev. E 67, 066203 (2003).

easier with operators use Holstein-Primakoff transformation

|𝑓〉 |𝑕〉

𝑑𝑓 𝑑𝑕 𝑇+ = 𝑑𝑓

†

𝑑𝑕 𝑇− = 𝑑𝑕

†

𝑑𝑓

𝑇𝑨 = ( 𝑑𝑓 𝑑𝑓 − 𝑑𝑕

†

𝑑𝑕)/2

slide-16
SLIDE 16

relation:

single-mode noncls. & many-particle entangl.

[15] Clive Emary and Tobias Brandes, “Chaos and the quantum phase transition in the dicke model,” Phys. Rev. E 67, 066203 (2003).

easier with operators use Holstein-Primakoff transformation

|𝑓〉 |𝑕〉

𝑑𝑓 𝑑𝑕 𝑇+ = 𝑑𝑓

†

𝑑𝑕 𝑇− = 𝑑𝑕

†

𝑑𝑓

𝑇𝑨 = ( 𝑑𝑓 𝑑𝑓 − 𝑑𝑕

†

𝑑𝑕)/2

Holstein-Primakoff transformation representable with a single operator 𝑏

[15]

slide-17
SLIDE 17

relation:

single-mode noncls. & many-particle entangl.

[15] Clive Emary and Tobias Brandes, “Chaos and the quantum phase transition in the dicke model,” Phys. Rev. E 67, 066203 (2003).

easier with operators use Holstein-Primakoff transformation

|𝑓〉 |𝑕〉

𝑑𝑓 𝑑𝑕 𝑇+ = 𝑑𝑓

†

𝑑𝑕 𝑇− = 𝑑𝑕

†

𝑑𝑓

𝑇𝑨 = ( 𝑑𝑓 𝑑𝑓 − 𝑑𝑕

†

𝑑𝑕)/2

Holstein-Primakoff transformation representable with a single operator 𝑏

[15] 𝑶 → ∞ 𝑶 → ∞

slide-18
SLIDE 18

relation:

single-mode noncls. & many-particle entangl.

[12] M.E. Tasgin , arXiv:1502.00988v1.

Holstein-Primakoff transformation

𝑶 → ∞ 𝑶 → ∞ implies [12] 𝑦 = ( 𝑏†+ 𝑏)/√2 spin-squeezing criterion quadrature-squeezing criterion

slide-19
SLIDE 19

the big picture: (i) & (ii) & (iii) together

DGCZ criterion

B.S.

two-mode

quadrature squeezing criterion

single-mode

number sqz criterion

single-mode

H&Z criterion

two-mode

B.S.

spin-squeezing criterion

many-particle

𝝄𝒐𝒇𝒙 ???

criterion

many-particle

H.P. H.P.

slide-20
SLIDE 20

the big picture: (i) & (ii) & (iii) together

DGCZ criterion

B.S.

two-mode

quadrature squeezing criterion

single-mode

number sqz criterion

single-mode

H&Z criterion

two-mode

B.S.

spin-squeezing criterion

many-particle

𝝄𝒐𝒇𝒙 ???

criterion

many-particle

H.P. H.P. 𝑶 → ∞ 𝑶 → ∞ 𝝄𝒐𝒇𝒙 ???

slide-21
SLIDE 21

the big picture: (i) & (ii) & (iii) together

DGCZ criterion

B.S.

two-mode

quadrature squeezing criterion

single-mode

number sqz criterion

single-mode

H&Z criterion

two-mode

B.S.

spin-squeezing criterion

many-particle

𝝄𝒐𝒇𝒙 ???

criterion

many-particle

H.P. H.P. 𝑶 → ∞ 𝑶 → ∞ 𝝄𝒐𝒇𝒙 ??? try calculating 〈 𝚬 𝑺

𝟑〉 = 〈 𝚬

𝑻+ 𝑻−

𝟑〉

derived by calculating 〈 𝚬 𝑻𝒚

𝟑〉

slide-22
SLIDE 22

new many-particle inseparability criterion: 𝝄𝒐𝒇𝒙

B.S.

number sqz criterion

single-mode

H&Z criterion

two-mode

𝝄𝒐𝒇𝒙 ???

criterion

many-particle

H.P. 𝑶 → ∞ 𝝄𝒐𝒇𝒙 ??? try calculating 〈 𝚬 𝑺

𝟑〉 = 〈 𝚬

𝑻+ 𝑻−

𝟑〉

if separable many-particle inseparable

slide-23
SLIDE 23

new many-particle inseparability criterion: 𝝄𝒐𝒇𝒙

DGCZ criterion

B.S.

two-mode

quadrature squeezing criterion

single-mode

number sqz criterion

single-mode

H&Z criterion

two-mode

B.S.

spin-squeezing criterion

many-particle

𝝄𝒐𝒇𝒙 ???

criterion

many-particle

H.P. H.P. 𝑶 → ∞ try calculating 〈 𝚬 𝑺

𝟑〉 = 〈 𝚬

𝑻+ 𝑻−

𝟑〉

derived by calculating 〈 𝚬 𝑻𝒚

𝟑〉

slide-24
SLIDE 24

new many-particle inseparability criterion: 𝝄𝒐𝒇𝒙

slide-25
SLIDE 25

Outline

  • Relation among

i. single-mode nonclassicality ii. two-mode entanglement iii. many-particle entanglement

  • new N-particle entanglement criterion

i. test for Dicke states ii. test for the ground state Dicke Hamilonian (superradiance) iii. test for single-photon superradiance (exact, time depndt)

  • iv. test for random superposition of Dicke states

v. ground state of an interacting BEC

slide-26
SLIDE 26

𝝄𝒐𝒇𝒙

Dicke states.

many-particle inseparable

𝑅 > 0 ⇒ entangled 𝜊Duan > 0 ⇒ entangled

slide-27
SLIDE 27

ground state of the Dicke Hamiltonian (superradiance)

𝝄𝒐𝒇𝒙

superradiance (superpositions of Dicke states)

𝜊Duan also fails 𝑅 > 0 ⇒ entangled 𝜊spin < 0 ⇒ entangled

(not plotted)

𝜊n𝑓𝑥 < 0 ⇒ entangled

slide-28
SLIDE 28

ground state of the Dicke Hamiltonian (superradiance)

𝝄𝒐𝒇𝒙

superradiance (superpositions of Dicke states)

ensemble-field entanglement

𝜈𝑜𝑓𝑥 < 0 ⇒ ensemble-field entanglement superradiance

slide-29
SLIDE 29

𝝄𝒐𝒇𝒙

single-photon superradiance: timed (superpositions of Dicke states) single-photon superradiance

randomly placed 2000 atoms

[16] Anatoly Svidzinsky and Jun-Tao Chang, “Cooperative spontaneous emission as a many-body eigenvalue problem,“ Phys. Rev. A 77, 043833 (2008). [17] Marlan O Scully, \Single photon subradiance: Quantum control of spontaneous emission and ultrafast readout,“ Physical Review Letters 115, 243602 (2015).

exactly solvable initially superposition of different atoms’ excitations

slide-30
SLIDE 30

𝝄𝒐𝒇𝒙

single-photon superradiance: timed (superpositions of Dicke states) single-photon superradiance

randomly placed 2000 atoms exactly solvable initially superposition of different atoms’ excitations

slide-31
SLIDE 31

𝝄𝒐𝒇𝒙 (random superpositions of Dicke states)

2000 random superposition of Dicke states witnessed in all when Q>0

slide-32
SLIDE 32

𝝄𝒐𝒇𝒙

interacting BEC

K.E. & trap potential atom-atom collisions bunching of atoms entanglement of atoms

slide-33
SLIDE 33

𝝄𝒐𝒇𝒙

interacting BEC

K.E. & trap potential atom-atom collisions bunching of atoms entanglement of atoms Ketterle [18] showed BEC responses collectively to an excitation if 𝑽𝒋𝒐𝒖 > 𝑭𝒇𝒚𝒅

[18] J. Stenger, S. Inouye, Ananth P Chikkatur, DM Stamper-Kurn, DE Pritchard, and W. Ketterle, Bragg spectroscopy of a bose-einstein condensate," Phys. Rev. Lett. 82, 4569 (1999).

slide-34
SLIDE 34

a question in place (answer)

[6] M. E. Tasgin and P. Meystre, “Spin sqz with coherent light via ent. swapping,” Phys. Rev. A 83, 053848 (2011).

  • perate

generates many-particle entanglement

  • perate

cannot generate entanglement

  • perate
  • perate

generates two-mode entanglement cannot generate two-mode entanglement

beam-splitter Hmlt answer is in becomes beam-splitter becomes two-mode sqz