Tunable Quantum Criticality in Multicomponent Rydberg Arrays

Arrays of Rydberg atoms have appeared as a remarkably rich playground to study quantum phase transitions in one dimension. One of the biggest puzzles that was brought forward in this context are chiral phase transitions out of density waves. Theoretically predicted chiral transition out of period-four phase is still pending experimental verification mainly due to extremely short interval over which this transition is realized in a single-component Rydberg array. In this Letter, we show that multicomponent Rydberg arrays with extra experimentally tunable parameters provide a mechanism to manipulate quantum critical properties without breaking translation symmetry explicitly. We consider an effective blockade model of two component Rydberg atoms. Weak and strong components obey nearest- and next-nearest-neighbor blockades correspondingly. When laser detuning is applied to either of the two components the system is in the period-3 and period-2 phases. But laser detuning applied to both components simultaneously stabilizes the period-4 phase partly bounded by the chiral transition. We show that relative ratio of the Rabi frequencies of the two components tunes the properties of the conformal Ashkin-Teller point and allows us to manipulate an extent of the chiral transition. The prospects of multicomponent Rydberg arrays in the context of critical fusion is briefly discussed.

Figure 1

Nature of the quantum phase transition between the period-four and disordered phases. Vertical axis states for some relevant operator that brings a system from the disordered phase to the period-4 phase. Orange line states for the conformal Ashkin-Teller transition. Yellow and orange regions at finite chiral perturbations correspond to direct chiral and Ashkin-Teller transitions. Blue and red surfaces indicate Pokrovsky-Talapov and Kosterlitz-Thouless transitions with a floating phase between the two. Green line states for the Lifshitz line.

Figure 2

Sketch of the two-component Rydberg atom. (a) Atoms are excited to the two Rydberg levels $\alpha =1$, 2 from the ground state by a laser with Rabi frequency ${\mathrm{\Omega }}_{\alpha }$ and detuning ${\mathrm{\Delta }}_{\alpha }$. (b) Interaction within the strong (magenta) and weak (blue) components result in nearest- and next-nearest-neighbor blockades. Configurations that violate these blockades are marked with red ellipses.

Figure 3

Phase diagrams of the blockade models defined by Eqs. (2a) and (2b) as a function of laser detuning of two species and for three relative ratio of Rabi frequencies ${\mathrm{\Omega }}_1/{\mathrm{\Omega }}_2$. Each phase diagram contains four gapped phases: the disordered phase, and three density wave phases with periodicity $p=2$, 3, and 4. Typical patterns of these phases are sketched in (a) where white circles denote atoms in the ground state, and blue and red circles denote the states for atoms excited to the first (weak) and second (strong) Rydberg levels, correspondingly. The period-2 phase is separated from the disordered and period-4 phases by two Ising transitions (blue squares and diamonds). The multicritical point (open orange circle) belongs to the Ashkin-Teller universality class. For some interval in (a) and (b) the transition to the period-4 phase is direct and chiral (red line). The key observation is that the extent of the chiral transition in (b) for ${\mathrm{\Omega }}_1/{\mathrm{\Omega }}_2=2$ is significantly larger than in (a) for ${\mathrm{\Omega }}_1/{\mathrm{\Omega }}_2=1$, while for ${\mathrm{\Omega }}_1/{\mathrm{\Omega }}_2=0.5$ in (c) the floating phase (gray) opens immediately. The transition between the period-three phase and the disordered phase is chiral (purple line) for small values of ${\mathrm{\Delta }}_1/{\mathrm{\Omega }}_1$ and through a floating phase (gray) for large detuning of the weak component (see “Methods ” for details).

Figure 4

Inverse correlation length $1/\xi$ and product $|q-\pi /2|\times \xi$ along various cuts across the transition (a)–(d) for ${\mathrm{\Omega }}_1/{\mathrm{\Omega }}_2=1$; (e)–(h) for ${\mathrm{\Omega }}_1/{\mathrm{\Omega }}_2=2$; and (i), (j) for ${\mathrm{\Omega }}_1/{\mathrm{\Omega }}_2=0.5$. (a), (b), (e), (f), (i) and pale symbols in (j): vertical cut through the Ashkin-Teller point. (c), (g): vertical cuts through chiral transitions. (d), (h) and bright symbols in (j): a cut through a floating phase. In (a) and (e) correlation lengths are fitted with the power law with equal critical exponents $\nu ={\nu }^{\prime }$ specified in each panel. $|q-\pi /2|\times \xi$ is defined with error bars $2\times {\xi }^2/N^2$; we only show error bars if they exceed the size of the symbols. Dashed lines show the boundary of the ordered phase extracted by fitting the correlation length, color code corresponds to the legend in the lower part of the figure.