Quantum simulation of interaction blockade in a two-site Bose–Hubbard system with solid quadrupolar crystal

Abstract

The Bose-Hubbard model provides an excellent platform for exploring exotic quantum coherence. Interaction blockade is an important fundamental phenomenon in the two-site Bose-Hubbard system (BHS), which gives a full quantum description for the atomic Bose-Josephson junction. Using the analogy between the two-site BHS and the quadrupolar nuclear magnetic resonance (NMR) crystal, we experimentally simulate a two-site Bose-Hubbard system in a NMR quantum simulator composed of the quadrupolar spin-3/2 sodium nuclei of a NaNO 3 single crystal, and observe the interesting phenomenon of interaction blockade via adiabatic dynamics control. To our best knowledge, this is the first experimental implementation of the quantum simulation of the interaction blockade using quadrupolar nuclear system. Our work exhibits important applications of quadrupolar NMR in the quantum information science, i.e. a spin-3/2 system can be used as a full 2-qubit su(4) system, if the quadrupole moment is not fully averaged out by fast tumbling in the liquid phase.

Experimental demonstration of nonlinear quantum metrology with optimal quantum state

“…In the following, we demonstrate the nonlinear phase accumulation process within an NMR experiment and show the dependence of phase uncertainty on the selection of m 1 and m 2 . Our experimental results are consistent with the above theoretical analysis, when the quadrupolar NMR system is mapped to an N spin-1/2 system [47].…”

“…We consider an input state in the form of jW in i ¼ P I m¼ÀI C m jI; mi, where jI; mi is eigenstate ofÎ a with eigenvalue m (ÀI 6 m 6 I), which can be mapped as the Dicke basis of two-site Bose-Hubbard system (BHS) with total particle number N ¼ 2I [47]. By analogy, the eigenvalue m corresponds to the half particle-number difference between two sites, and the Dicke basis jI; mi ¼ jI À m; I þ mi represents I À m particles in site a while I þ m particles in site b.…”

NMR Hamiltonian as an effective Hamiltonian to generate Schrödinger's cat states

“…However, from an experimental point of view, there are other requirements to do that, such as the ability to access information about the system's quantum state. This is achieved on arrangements of spin systems with a spatial order, as happens in solid crystals [27,28,39,45], at different semiconductor platforms [46][47][48][49], nitrogen vacancies reported by many groups [50][51][52][53][54][55], and liquid crystals [56].…”

“…( 1) fits the definition of a nuclear quadrupolar Hamiltonian [22,23]. From their similar qualities, the nuclear spin counterpart has been explored in many quantum information applications, such as the quantum simulation of a Bose-Einstein condensate of one mode [24], the definition of coherent states in the context of nuclear spin [25], and others [18,[26][27][28].…”

Multiparticle Wannier states and Thouless pumping of interacting bosons

“…Topologically resonant tunnelings.-Below we discuss the Thouless pumping associated with the isolated band A. If U ≫ (J, δ), the bound state breaks down and resonant tunneling happens between |2 j and |1 j |1 j+1 or |1 j−1 |1 j when U is comparable to 2∆ [50][51][52]. Here, |1 j |1 k is short for |0, ..., 1 j , ..., 1 k , ..., 0 .…”