Phase and Amplitude Modes in the Anisotropic Dicke Model with Matter Interactions

Romero, Ricardo Herrera; Bastarrachea-Magnani, Miguel Angel

doi:10.3390/e26070574

Phase and Amplitude Modes in the Anisotropic Dicke Model with Matter Interactions

Jun 11, 2024

17 pages

Published in:

Entropy 26 (2024) 7, 574

Published: Jul 3, 2024

e-Print:

2406.09446 [quant-ph]

DOI:

10.3390/e26070574

View in:

ADS Abstract Service

reference search1 citation

Citations per year

Abstract: (MDPI)

Phase and amplitude modes, also called polariton modes, are emergent phenomena that manifest across diverse physical systems, from condensed matter and particle physics to quantum optics. We study their behavior in an anisotropic Dicke model that includes collective matter interactions. We study the low-lying spectrum in the thermodynamic limit via the Holstein–Primakoff transformation and contrast the results with the semi-classical energy surface obtained via coherent states. We also explore the geometric phase for both boson and spin contours in the parameter space as a function of the phases in the system. We unveil novel phenomena due to the unique critical features provided by the interplay between the anisotropy and matter interactions. We expect our results to serve the observation of phase and amplitude modes in current quantum information platforms.

Note:

17 pages, 4 figures

Dicke model
interacting qubits
quantum phase transitions
phase mode
amplitude mode
geometric phase

References(177)

Figures(4)

[1]

Plasmons, Gauge Invariance, and Mass

Philip W. Anderson
(
- Bell Labs
)

- Phys.Rev. 130 (1963) 439-442,
- Also in *Farhi, E. (ed.), Jackiw, R. (ed.): Dynamical Gauge Symmetry Breaking*, 48-51,
•
DOI:
- 10.1103/PhysRev.130.439

[2]

Broken Symmetries and the Masses of Gauge Bosons

Peter W. Higgs
(
- Edinburgh U.
)

- Phys.Rev.Lett. 13 (1964) 508-509,
- Also in *Lichtenberg, D. B. (Ed.), Rosen, S. P. (Ed.): Developments In The Quark Theory Of Hadrons, Vol. 1*, 155-156,
•
DOI:
- 10.1103/PhysRevLett.13.508

[3]

Field Theories with Superconductor Solutions

J. Goldstone
(
- CERN
)

- Nuovo Cim. 19 (1961) 154-164,
- Also in *Lai, C. H. (ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 93-103
•
DOI:
- 10.1007/BF02812722

[4]

Dynamical model of elementary particles based on an analogy with superconductivity. II.

Yoichiro Nambu
(
- Chicago U., EFI
)
,
G. Jona-Lasinio
(
- Chicago U., EFI
)

- Phys.Rev. 124 (1961) 246-254,
•
DOI:
- 10.1103/PhysRev.124.246

[5]

Gauge-Invariant Theory of the Dynamical Interaction of Charge Density Waves and Superconductivity

- Phys.Rev.Lett. 47 (1981) 11, 811-814
•
DOI:
- 10.1103/PhysRevLett.47.811

[6]

Amplitude collective modes in superconductors and their coupling to charge-density waves

P.B. Littlewood
,
C.M. Varma

- Phys.Rev.B 26 (1982) 4883-4893
•
DOI:
- 10.1103/PhysRevB.26.4883

[7]

Higgs Boson in Superconductors

C.M. Varma

- J.Low Temp.Phys. 126 (2002) 901-909
•
DOI:
- 10.1023/A:1013890507658

[8]

Amplitude / Higgs Modes in Condensed Matter Physics

- Ann.Rev.Condensed Matter Phys. 6 (2015) 269
•
e-Print:
- 1406.2968
•
DOI:
- 10.1146/annurev-conmatphys-031214-014350

[9]

Amplitude Higgs mode in the 2H-NbSe $_{2}$ superconductor

M.A. Méasson
,
Y. Gallais
,
M. Cazayous
,
B. Clair
,
P. Rodière

et al.

- Phys.Rev.B 89 (2014) 060503
•
DOI:
- 10.1103/PhysRevB.89.060503

[10]

Theory of two-dimensional quantum Heisenberg antiferromagnets with a nearly critical ground state

Andrey V. Chubukov
(
- Yale U. and
- Moscow, Inst. Phys. Problems
)
,
Subir Sachdev
(
- Yale U.
)
,
Jinwu Ye
(
- Yale U.
)

- Phys.Rev.B 49 (1994) 11919-11961
•
e-Print:
- cond-mat/9304046
•
DOI:
- 10.1103/PhysRevB.49.11919

[11]

Spectral functions of the Higgs mode near two-dimensional quantum critical points

Daniel Podolsky
(
- Technion
)
,
Subir Sachdev
(
- Harvard U., Phys. Dept. and
- Leiden U.
)

- Phys.Rev.B 86 (2012) 054508
•
e-Print:
- 1205.2700
•
DOI:
- 10.1103/PhysRevB.86.054508

[12]

Quantum Magnets under Pressure: Controlling Elementary Excitations in TlCu Cl-3

Ch. Ruegg
(
- University Coll. London
)
,
B. Normand
(
- Fribourg U. and
- Zurich, ETH
)
,
M. Matsumoto
(
- Unlisted
)
,
A. Furrer
(
- Zurich, ETH and
- PSI, Villigen
)
,
D.F. McMorrow
(
- University Coll. London
)

et al.

- Phys.Rev.Lett. 100 (2008) 205701
•
e-Print:
- 0803.3720
•
DOI:
- 10.1103/PhysRevLett.100.205701

[13]

Broken Symmetry and the Mass of Gauge Vector Mesons

F. Englert
(
- Brussels U.
)
,
R. Brout
(
- Brussels U.
)

- Phys.Rev.Lett. 13 (1964) 321-323,
- Also in *Lai, C. H. (ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 127-129,
•
DOI:
- 10.1103/PhysRevLett.13.321

[14]

Global Conservation Laws and Massless Particles

G.S. Guralnik
(
- Imperial Coll., London
)
,
C.R. Hagen
(
- Imperial Coll., London
)
,
T.W.B. Kibble
(
- Imperial Coll., London
)

- Phys.Rev.Lett. 13 (1964) 585-587,
- Also in *Lai, C. H. (ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 130-132,
•
DOI:
- 10.1103/PhysRevLett.13.585

[15]

Spontaneous symmetry breaking, gauge theories, the higgs mechanism and all that

J. Bernstein
(
- Stevens Tech.
)

- Rev.Mod.Phys. 46 (1974) 7-48,
- Rev.Mod.Phys. 47 (1975) 259-259 (erratum),
- Rev.Mod.Phys. 46 (1974) 855-855 (erratum)
•
DOI:
- 10.1103/RevModPhys.46.7

[16]

Quantum Phase Transitions

S. Sachdev

[17]

Understanding Quantum Phase Transitions

L.D. Carr

[18]

Controlling Discrete and Continuous Symmetries in “Superradiant” Phase Transitions with Circuit QED Systems

- Phys.Rev.Lett. 112 (2014) 17, 173601
•
e-Print:
- 1310.3780
•
DOI:
- 10.1103/PhysRevLett.112.173601

[19]

Goldstone and Higgs modes of photons inside a cavity

Yi-Xiang Yu
(
- Mississippi State U. and
- Beijing, Inst. Phys.
)
,
Jinwu Ye
(
- Mississippi State U. and
- Capital Normal U., Beijing
)
,
Wuming Liu
(
- Beijing, Inst. Phys.
)

- Scientific Reports 3 (2013) 3476
•
e-Print:
- 1312.3404
•
DOI:
- 10.1038/srep03476

[20]

Detecting the Amplitude Mode of Strongly Interacting Lattice Bosons by Bragg Scattering

U. Bissbort
,
S. Götze
,
Y. Li
,
J. Heinze
,
J.S. Krauser

et al.

- Phys.Rev.Lett. 106 (2011) 205303
•
DOI:
- 10.1103/PhysRevLett.106.205303

[21]

The `Higgs' Amplitude Mode at the Two-Dimensional Superfluid-Mott Insulator Transition

et al.

- Nature 487 (2012) 454-458
•
e-Print:
- 1204.5183
•
DOI:
- 10.1038/nature11255

[22]

Monitoring and manipulating Higgs and Goldstone modes in a supersolid quantum gas

J. Léonard
,
A. Morales
,
P. Zupancic
,
T. Donner
,
T. Esslinger

- Science 358 (2017) 1415-1418
•
DOI:
- 10.1126/science.aan2608

[23]

Emergence of continuous rotational symmetries in ultracold atoms coupled to optical cavities

E.I.R. Chiacchio
,
A. Nunnenkamp

- Phys.Rev.A 98 (2018) 023617
•
DOI:
- 10.1103/PhysRevA.98.023617

[24]

Supersolid Properties of a Bose-Einstein Condensate in a Ring Resonator

S.C. Schuster
,
P. Wolf
,
S. Ostermann
,
S. Slama
,
C. Zimmermann

- Phys.Rev.Lett. 124 (2020) 143602
•
DOI:
- 10.1103/PhysRevLett.124.143602

[25]

On the superradiant phase transition for molecules in a quantized radiation field: the dicke maser model

- Annals Phys. 76 (1973) 2, 360-404
•
DOI:
- 10.1016/0003-4916(73)90039-0

1-25 of 177
1
2
3
4
5
•••
8
25 / page

Phase and Amplitude Modes in the Anisotropic Dicke Model with Matter Interactions

Citations per year

Amplitude collective modes in superconductors and their coupling to charge-density waves

Higgs Boson in Superconductors

Amplitude Higgs mode in the 2H-NbSe2_{2}2​ superconductor

Quantum Phase Transitions

Understanding Quantum Phase Transitions

Detecting the Amplitude Mode of Strongly Interacting Lattice Bosons by Bragg Scattering

Monitoring and manipulating Higgs and Goldstone modes in a supersolid quantum gas

Emergence of continuous rotational symmetries in ultracold atoms coupled to optical cavities

Supersolid Properties of a Bose-Einstein Condensate in a Ring Resonator

Amplitude Higgs mode in the 2H-NbSe $_{2}$ superconductor