[Paper Review] Particle-Hole Pair Coherence in Mott Insulator Quench Dynamics

Khan W. Mahmud, Lei Jiang+2 more|arXiv (Cornell University)|Jan 26, 2014

Cold Atom Physics and Bose-Einstein Condensates44 references3 citations

TL;DR

This paper predicts novel collapse-and-revival (CR) oscillations in quenched Mott insulator states due to short-range off-diagonal coherence from particle-hole pairs. Upon sudden lattice quenching, the quasi-momentum distribution oscillates between maximum occupation at $k=0$ and the Brillouin zone edge ($k=\pi$), with visibility becoming negative—distinct from superfluids—due to coherent doublon-holon pairs, a signature observable in ultracold atoms and robust under dephasing.

ABSTRACT

We predict the existence of novel collapse and revival oscillations that are a distinctive signature of the short-range off-diagonal coherence associated with particle-hole pairs in Mott insulator states. Starting with an atomic Mott state in a one-dimensional optical lattice, suddenly raising the lattice depth freezes the particle-hole pairs in place and induces phase oscillations. The peak of the quasi-momentum distribution, revealed through time of flight interference, oscillates between a maximum occupation at zero quasi-momentum (the $Γ$ point) and the edge of the Brillouin zone. We show that the population enhancements at the edge of the Brillouin zone is due to coherent particle-hole pairs, and we find similar effects for fermions and Bose-Fermi mixtures in a lattice. Our results open a new avenue for probing strongly correlated many-body states with short-range phase coherence that goes beyond the familiar collapse and revivals previously observed in the long-range coherent superfluid regime.

Motivation & Objective

• To identify and characterize a new type of collapse-and-revival dynamics in Mott insulators, distinct from those in superfluids.
• To demonstrate that short-range phase coherence from particle-hole pairs induces measurable oscillations in quasi-momentum distribution after a quench.
• To show that this dynamics is robust under realistic dephasing and trapping effects, making it experimentally accessible.
• To extend the phenomenon to fermions at half-filling and Bose-Fermi mixtures with integer total filling.
• To provide a new probe for short-range coherence in strongly correlated quantum matter beyond superfluid-like behavior.

Proposed method

• Sudden quench of optical lattice depth to freeze particle-hole pairs and induce phase evolution in the many-body wavefunction.
• Numerical simulations using infinite time-evolving block decimation (i-TEBD) and exact diagonalization for 1D lattices with up to four sites.
• Analysis of time-resolved quasi-momentum distributions $n_k(t)$ and visibility $\mathcal{V}(t) = \frac{n_{k=\pi}(t) - n_{k=0}(t)}{n_{k=0}(t) + n_{k=\pi}(t)}$ to detect revivals and coherence signatures.
• Use of strong-coupling expansion (SCE) theory to validate numerical results in the deep Mott insulator regime.
• Inclusion of dephasing mechanisms such as finite post-quench tunneling, effective multi-body interactions, and harmonic trapping in simulations.
• Comparison of dynamics in bosonic Mott insulators, spinless fermions at half-filling, and Bose-Fermi mixtures with total site occupation $n_{\text{tot}}=1$.

Experimental results

Research questions

• RQ1 Can collapse-and-revival oscillations emerge in Mott insulators despite their short-range coherence, contrary to the conventional view that CR is exclusive to superfluids?
• RQ2 What is the role of particle-hole pairs (doublons and holons) in generating the observed oscillations in the quasi-momentum distribution?
• RQ3 How does the visibility $\mathcal{V}(t)$ behave in quenched Mott insulators, and can it become negative, indicating $k=\pi$ revivals?
• RQ4 Is the novel CR dynamics robust under realistic experimental imperfections such as dephasing and harmonic trapping?
• RQ5 Do fermionic and Bose-Fermi mixture systems with integer filling exhibit similar dynamics due to correlated particle-hole pairs?

Key findings

• The quasi-momentum distribution exhibits revivals at the Brillouin zone edge ($k=\pi$) after a quench, with the peak population at $k=\pi$ exceeding that at $k=0$ at certain times.
• The visibility $\mathcal{V}(t)$ becomes negative in the Mott insulator regime, indicating that $n_{k=\pi}(t) > n_{k=0}(t)$, a signature absent in superfluid quenches.
• The visibility oscillates sinusoidally in time for Mott insulators, contrasting with the exponential decay seen in superfluid quenches.
• Condensate fraction $f_c(t)$ shows novel kinks due to oscillations between symmetric and antisymmetric natural orbitals of the single-particle density matrix.
• The effect is robust under finite post-quench tunneling, effective multi-body interactions, and harmonic trapping, provided the Mott plateau is sufficiently large.
• The dynamics are observed in bosons, spinless fermions at half-filling, and Bose-Fermi mixtures with total site occupation $n_{\text{tot}}=1$, indicating universality of the mechanism.