MM2020:D17.00009

1. Realizing Discrete Time Crystals
in Quantum Dot Spin Arrays
with Magnetic Field Gradients
Bikun Li
Collaborators:
Ada Warren
John Van Dyke
Edwin Barnes
Sophia Economou
[PhysRevB.101.115303]APS March Meeting
2020

2. Content
• Introduction: What is discrete time crystal?
• Model and Realization
• Results

3. What is Discrete Time Crystal?
• Robust Floquet system that ‘breaks time translational symmetry’.
• Many body system that fail to thermalize. → preserving information.
• Realizations with multi-spin systems (with ion trap, mostly based on Ising interaction).
[J. Zhang, et al., Nature 543, 217–220(2017)]
[F. Wilczek PRL. 109, 160401, Patrick Bruno, PRL.111.070402]
[D. V. Else, et al., PRL 117, 090402 (2016)]
[N. Y. Yao, PRL. 118, 030401 (2017)]
Relevant references:
Oscillating
Observables

4. Realization on quantum dot system
• Advantage
• Relatively mature technology
• Highly integrated
• Challenges:
• Can we apply Strong disorder?
• Heisenberg instead of Ising interaction
*Original undriven Hamiltonian:
[Y. P. Kandel, et al., Nature 573, 553–557(2019)]
[A. R. Mills, et al., Nat Commun 10, 1063 (2019)]
An approach to convert ‘Heisenberg’ back to ‘Ising’ (H2I):
[E. Barnes, et al., PRB 99, 035311]
Heisenberg interaction gives less
integrability on individual spin.

5. Realization on quantum dot system
[Y. P. Kandel, et al., Nature 573, 553–557(2019)]
[A. R. Mills, et al., Nat Commun 10, 1063 (2019)]
Solution: strong gradient field
• Only weak disorder is needed.
• Effective Ising interaction.
[B. Li, et al., PhysRevB.101.115303]
(1)Strong gradient magnetic
field is commonly implemented
by micro magnet.
(2) Theoretical researches
of Stark localization
implied the feasibility.
[M.Schulz, et al, PRL. 122, 040606 (2019)]
[E. van Nieuwenburg, Proc. Natl. Acad. Sci. 116, 9269 (2019).]

6. Our Model & Theoretical Results
Hamiltonian:
‘gradient field’ that realize ‘Stark localization’
Stroboscopic Effective Hamiltonian: (t = 2sT)
[B. Li, et al., arXiv:1912.05130]
*Necessary condition of robust DTC phase : (non-zero quasi energy gap)
Local spin flipping perturbation
Implemented by micro magnet
Due to nuclear spin-bath
(Square wave packet of AC field)
Global pi-pulse sequence

7. Numerical Results
(Different colors for different sites, edge spins have better performance of longevity.)
Number of Floquet periods (t/T)
Expectationvalueofσz
atevenperiod2sT
(practical data from Rochester team)
(longevity time scale)
[B. Li, et al., PhysRevB.101.115303]

8. Statistical results of longevity of
local observables :
The mechanism of exponential longevity is
explained as: global flipping of all spin needs
an L-th high order process, which has a
suppressed amplitude for tunneling.
Sampling: 1000 disorder
realizations, with L = 6.
Sampling: 200 disorder
realizations
[B. Li, et al., PhysRevB.101.115303]
Numerical Results
gradient
Longevitytimescale

9. The ‘Phase diagrams’ that indicate the parameters that give DTC phase (yellow) , where observables are well
preserved for >> 400 periods:
Sampling: 100 disorder realizations,
When ε→0, instabilities (purple) happen as
Numerical Results
Large J interferes the pi-pulse
Pulseerror
Interaction
Results of
different site (j)
and gradient (g)
are compared
[B. Li, et al., PhysRevB.101.115303]
*These results are obtained from uniform J.
Disordered J will destroy this periodicity, but it could provide a more stable DTC for all |ψ0>

10. Summary
• We proposed the idea of realizing DTC on quantum dot system.
• Numerical results are given, self-consistent theoretical analysis is
given as well, which verify the availability of our model.
Thanks for your attention!