Quench Dynamics of a Fermi Gas with Strong Nonlocal Interactions

We induce strong nonlocal interactions in a 2D Fermi gas in an optical lattice using Rydberg dressing. The system is approximately described by a $t-V$ model on a square lattice where the fermions experience isotropic nearest-neighbor interactions and are free to hop only along one direction. We measure the interactions using many-body Ramsey interferometry and study the lifetime of the gas in the presence of tunneling, finding that tunneling does not reduce the lifetime. To probe the interplay of nonlocal interactions with tunneling, we investigate the short-time-relaxation dynamics of charge-density waves in the gas. We find that strong nearest-neighbor interactions slow down the relaxation. Our work opens the door for quantum simulations of systems with strong nonlocal interactions such as extended Fermi-Hubbard models.

Popular Summary

Ultracold atoms in optical lattices have served as a flexible platform for quantum simulation of condensed-matter phenomena for years. In these experiments, neutral atoms placed in periodic patterns of light simulate the behavior of strongly interacting electrons in solid-state crystals. However, the platform has been mostly limited to a class of problems where interactions are only contactlike in nature. Recent efforts have been dedicated to increasing the range of interactions to achieve simulations of a larger class of systems. Here, we engineer tunable long-range interactions to simulate fermions in a 2D lattice interacting with fermions at other sites in the lattice.

In our experiment, we use the intensity and frequency of a laser to control the interaction potential between atoms in a cold gas. We load lithium atoms into an optical lattice and then excite them with UV laser light. This light is tuned to “dress” the atoms, that is, put them into a superposition of the ground state and a highly excited state known as a Rydberg state. When in this state, atoms exhibit exceptionally strong long-range interactions.

We show that by tuning the intensity of this “dressing” light, we have real-time control over interactions among the atoms. Using this platform, we simulate fermions with strong off-site interactions in a 2D lattice and observe a clear effect of the interactions slowing down the density relaxation dynamics in the gas.

Our experiment opens the door for quantum simulations of systems exhibiting many interesting quantum many-body phenomena, including quantum magnetism, topological superfluidity, and supersolidity.

Figure 1

Realization of a $t-V$ model with Rydberg dressing. (a) The Rydberg-dressing beam propagates along the $x$ direction of the lattice, effectively decoupling 1D chains in the $y$ direction due to a differential lightshift. Hopping of fermions (red dots) along the $x$ direction is unaffected. Interactions are isotropic. (b) ${}^6\mathrm{Li}$ pair potentials for dressing to the state $|28P,m_l=0,m_s=-1/2⟩$ calculated using Ref. [50]. The color of the lines represents the overlap with the target pair state ($|28P,0,-1/2⟩\otimes |28P,0,-1/2⟩$) coupled via the laser with Rabi coupling $\mathrm{\Omega }$ and detuning $\mathrm{\Delta }$ from the target state. Inset: calculated dressed potential for $\mathrm{\Omega }=2\pi \times 7.66\mathrm{MHz}$ and $\mathrm{\Delta }=2\pi \times 35\mathrm{MHz}$ taking into account the overlaps to all pair potentials (orange solid line). The dashed green line represents the expected dressed potential for a simple van der Waals potential with $C_6=h\times 90.19\mathrm{MHz}$ $a_{\mathrm{latt}}^6$. Pink points are the interaction at each lattice distance taking into account the wave-function spread of the atoms.

Figure 2

Measuring Rydberg-dressed interactions with many-body Ramsey interferometry. (a) Energy level diagram for ${}^6\mathrm{Li}$ showing that the dressing of the other hyperfine ground state cannot be ignored. Here, $\mathrm{\Delta }/2\pi$ is varied between 30 and 100 MHz, while ${\mathrm{\Delta }}_0/2\pi =75.806(1)\mathrm{MHz}$. (b) Ramsey fringe frequency measured at a detuning of $\mathrm{\Delta }=2\pi \times 100\mathrm{MHz}$ at different positions in the cloud. The frequency is almost constant along the propagation direction of the beam (purple). In the transverse direction (yellow), it varies rapidly as expected for a tightly focused Gaussian beam. Insets: (i) Ramsey oscillations at two representative positions in the cloud. (ii) Sample image of one spin state in the cloud at $T=20\mu \mathrm{s}$. (c) Spin correlations for different spin-echo pulse times at $\mathrm{\Omega }=2\pi \times 7.66(7)\mathrm{MHz}$ and $\mathrm{\Delta }=2\pi \times 35\mathrm{MHz}$. Measurement (top) and theoretical expectation (bottom). (d) Nearest- (green) and next-nearest- (orange) neighbor correlations after subtracting $C(\infty )$. Lines correspond to the expected correlations. Experimental error bars correspond to standard error of the mean.

Figure 3

Lifetime of itinerant Rydberg-dressed fermions. (a) Atom number vs dressing time for a frozen gas. The red circles correspond to measurements on a system of ($7\times 7$) sites. Dashed-dotted line corresponds to an exponential fit to the first five data points, and dashed line corresponds to the expected single-particle dressed lifetime ${\tau }_{\mathrm{eff}}$. (b) Measured lifetime in a frozen gas in units of ${\tau }_{\mathrm{eff}}$ vs the initial density for $\mathrm{\Omega }=2\pi \times 9.25(8)\mathrm{MHz}$ and $\mathrm{\Delta }=2\pi \times [30(\mathrm{green}),40(\mathrm{purple}),60(\mathrm{orange})]\mathrm{MHz}$. Inset: same measurements in units of ms. (c) Lifetime vs initial density for different tunnelings: 0.01 kHz (green), 0.25 kHz (purple), 1.0 kHz (orange), and 1.7 kHz (pink). The data are taken with $\mathrm{\Omega }=2\pi \times 6.04(8)\mathrm{MHz}$, $\mathrm{\Delta }=2\pi \times 30\mathrm{MHz}$. Insets: (i) Tunneling dynamics of atoms sparsely initialized on a strip along the $y$ direction with no dressing light. From these data, we extract a tunneling rate $t=h\times 1.7\mathrm{kHz}$. (ii) Same measurement in the presence of the dressing light. (iii) Same measurement in the presence of the dressing light but with the strip along the $x$ direction. Experimental error bars correspond to the standard error of the mean.

Figure 4

Interaction dependence of quench dynamics of a charge-density wave. (a) Average initial state density profile for the quench measurements. (b) Density profile averaged along the $y$ direction of the initial state shown in (a). (c) Density profile time evolution for interactions $V/t=[0,0.78(7),1.61(8),2.9(2)]$. Color scale is the same as in (a). (d) Fitted relative amplitude of density profile vs time. Colors (green, orange, purple, and pink) correspond to the interactions in (c) from lowest to highest. (e) Autocorrelation function of the density pattern. Colors are the same as in (d). Shaded curves correspond to numerical simulations. Experimental error bars correspond to the standard error of the mean.

Figure 5

Density dependence of quench dynamics. (a) (Top) initial state density profiles; (bottom) corresponding time evolution of each initial state for $V/t=2.9(2)$. Color bar is the same as Fig. 4 with limits set by dotted lines on top panel. (b) Fitted relative amplitude of density profiles vs time. Colors (green, orange, purple, and pink) correspond to the initial states in (a) from low to high density. (c) Autocorrelation function of the density pattern. Colors are the same as in (b). Experimental error bars correspond to the standard error of the mean.

Figure 6

Role of interchain couplings in slowing down charge-density wave relaxation. Numerical simulations of a $t-V$ model with tunneling $t$ along only one direction and isotropic nearest-neighbor interactions $V$. (a) Fitted relative sinusoid amplitude to observed (circles) and calculated quench dynamics of $1\times 21$ systems (shaded regions). The colors represent the different interaction strengths $V/t=[0(\mathrm{green}),0.78(7)(\mathrm{orange}),1.61(8)(\mathrm{purple}),2.9(2)(\mathrm{pink})]$ explored in the experiment. (b) Same comparison as in (a) but for calculations done on $2\times 11$ systems. This plot is Fig. 4. Experimental error bars correspond to the standard error of the mean.

Figure 7

Rydberg dressing of ${}^6\mathrm{Li}$. (a) Level diagram showing the hyperfine ground states of ${}^6\mathrm{Li}$ directly coupled to the $28P$ Rydberg state using linearly ($\pi$) polarized light at a field of 592-G. The basis we use is $|m_l,m_s⟩$. (b) Rydberg-dressing scheme for two atoms in different hyperfine ground states $|1⟩$ and $|2⟩$ coupled to the Rydberg state $|r⟩$. $\mathrm{\Omega }$ is the Rabi coupling of the laser, $\mathrm{\Delta }$ is the detuning from the resonant transition between $|1⟩$ and $|r⟩$, ${\mathrm{\Delta }}_0$ is the hyperfine splitting between $|1⟩$ and $|2⟩$, and $V(R)=-C_6/R^6$ is the van der Waals interaction potential between two Rydberg states $|r⟩$.

Figure 8

Dependence of lifetime on atom number at fixed density. (a) Initial lifetime for 2D systems with different initial atom number dressed to $31P$. Measurements are made in a 2D rectangular system of small width approximately $4a_{\mathrm{latt}}$ and variable length along the dressing beam direction. We observe no strong dependence on the atom number. The Rabi frequency is approximately constant over the entire system. For these data, $\mathrm{\Omega }=2\pi \times 7.02(5)\mathrm{MHz}$, $\mathrm{\Delta }=2\pi \times 60\mathrm{MHz}$, and $n=0.8$. (b) Same as in (a) but for systems dressed to $40P$. For these data, $\mathrm{\Omega }=2\pi \times 5.6(2)\mathrm{MHz}$, $\mathrm{\Delta }=2\pi \times 40\mathrm{MHz}$, and $n=0.55$. Insets: raw data with exponential fit to extract the initial decay rate. Experimental error bars correspond to the standard error of the mean.

Figure 9

Atom loss during charge-density wave dynamics. (a) Atom number decay over the quenches shown in Fig. 5. Each color represents a set with a different initial density. Circles are measured data with error bars and lines are simple exponential decay fits. The dressing parameters are $\mathrm{\Omega }=2\pi \times 6.99(8)\mathrm{MHz}$ and $\mathrm{\Delta }=2\pi \times 30\mathrm{MHz}$. (b) Lifetime vs the initial average density of the charge-density wave as extracted from the data in (a). This behavior is in agreement with our observations shown in Fig. 3. Experimental error bars correspond to the standard error of the mean.