Complete population inversion of Bose particles by an adiabatic cycle

Talk at JPS spring meeting 2017

(In Japanese) 断熱サイクルによるボーズ粒子系の準位反転

Transcript

1. 1 / 14 Complete population inversion of Bose particles by an adiabatic cycle அ೤αΠΫϧʹΑΔϘʔζཻࢠܥͷ४Ґ൓స Atushi Tanaka (Tokyo Met. U.) and Taksu Cheon (Kochi U. Tech) ాதಞ࢘ (ट౎େཧ޻)ɺશ୎थ (ߴ஌޻Պେ) 2017-03-18 ೔ຊ෺ཧֶձ ୈ 72 ճ೥࣍େձ (2017-03-17/2017-03-20) େࡕେֶ ๛தΩϟϯύε (େࡕ෎๛தࢢ) 18aC11-8
2. 2 / 14 Outline Introduction One-body case (Kasumie, Miyamoto and AT 2016) Perturbative argument for many-body case (AT and TC 2016) Summary and outlook Ref. ▶ Kasumie, Miyamoto and AT, PRA 93, 042105 (2016). ▶ AT and TC, New J. Phys. 18, 045023 (2016).
3. Introduction 3 / 14 Exotic Quantum Holonomy for Adiabatic Cycles Quantum Holonomy Adiabatic cycles may induce nontrivial geometric phase factors, which is identified with the holonomy of fiber bundles. Ref. Berry 1984; Simon 1983. Exotic Quantum Holonomy Adiabatic cycles may induce nontrivial change in eigenspaces. This can be associated with a covering space (i.e., a fiber bundle with a discrete structure group). Ref. AT and TC, BUTSURI(೔ຊ෺ཧֶձࢽ) April 2017 (in printing)
4. Introduction 4 / 14 An adiabatic cycle may induce the population inversion. We will introduce an example of exotic quantum holonomy in weakly-interacting Bosons confined in a 1D space, where an adiabatic cycle C induces the population inversion. n = 1 n = 2 n = 3 Initial: |1⊗N⟩ C ⇒ Final: |2⊗N⟩ cf. Exotic quantum holonomy in Lieb-Liniger model (Yonezawa, AT and TC 2013)
5. One-body case (Kasumie, Miyamoto and AT 2016) 5 / 14 Introduction One-body case (Kasumie, Miyamoto and AT 2016) Perturbative argument for many-body case (AT and TC 2016) Summary and outlook
6. One-body case (Kasumie, Miyamoto and AT 2016) 6 / 14 Adiabatic cycle C (= C1 +C2 +C3) |ψ0 Prepare an initial state. C1 X1 Adiabatically insert a δ-wall at X1. C2 X1 X2 Adiabatically move the δ-wall from X1 to X2. C3 X2 Adiabatically remove the δ-wall at X2. |? The Hamiltonian returns to the initial one.
7. One-body case (Kasumie, Miyamoto and AT 2016) 7 / 14 Parametric evolution of eigenenergies (N = 1) |1⟩ and |2⟩ are connected by C. where ¯ k ∝ √ E/N (eigenenergies are scaled).
8. Perturbative argument for many-body case (AT and TC 2016) 8 / 14 Introduction One-body case (Kasumie, Miyamoto and AT 2016) Perturbative argument for many-body case (AT and TC 2016) Summary and outlook
9. Perturbative argument for many-body case (AT and TC 2016) 9 / 14 N-dependence of the energy levels? The scaled energy levels (¯ k ∝ √ E/N) of |n⊗N⟩ are independent of N, when the interparticle interaction is absent: Who disturbs the exotic quantum holonomy |1⊗N⟩ C → |2⊗N⟩? ▶ Other levels (e.g. |12⟩ or |112⟩) may cross with |n⊗N⟩. ▶ Even weak interparticle interactions may lift the degeneracies.
10. Perturbative argument for many-body case (AT and TC 2016) 10 / 14 N = 2: some crossings become avoided While |11⟩ C → |22⟩ is intact, the interaction destroys |33⟩ C → |44⟩. This is because the crossing between |33⟩ and |24⟩ become avoided. On the other hand, the crossings in C2 is intact because the gaps are, at most, exponentially small as they involves tunneling.
11. Perturbative argument for many-body case (AT and TC 2016) 11 / 14 N = 3: some crossings are robust thanks to a selection rule The exotic quantum holonomy from |111⟩ to |222⟩ is intact, although |222⟩ and |113⟩ cross: This is thanks to a selection rule of the interaction Hamiltonian V , i.e., ⟨222|V |113⟩ = 0, (a selection rule) when V consists of two-body interactions.
12. Perturbative argument for many-body case (AT and TC 2016) 12 / 14 N > 2: the holonomy |1⊗N⟩ C → |2⊗N⟩ survives N = 4 N = 2 Selection rule: V |2⊗N⟩ has nonzero overlap only with |2⊗N−2n1n2⟩, i.e., ⟨2⊗N|V |2⊗N−2n1n2⟩ ̸= 0. These two states nevertheless don’t cross as |22⟩ and |n1n2⟩ don’t cross.
13. Summary and outlook 13 / 14 Summary The adiabatic cycle C, where the strength and position of δ-potential is varied, induces the complete population inversion |1⊗N⟩ → |2⊗N⟩ of N Bosons, under the following assumptions ▶ Bosons are confined in a 1D-box. ▶ Two-body interparticle interactions are weak. For an arbitrary shape of the confinement potential, it is sufficient to reexamine the case N = 2, thanks to the selection rule. Ref. AT and TC, New J. Phys. 18, 045023 (2016).