 Thanks for the introduction. Hi, everyone. My name is Shi Dai. I'm from University of Waterloo. Today I'll be talking about dissipated london zener tunneling measurements. We have down where we have found evidence for a crossover from weak to strong environment coupling. This work is led by me and Robin from University of Waterloo. I help from others on device design and with Lincoln Lab for the device of fabrication and the experiment infrastructures as well as theory support from USC. The london zener problem is a famous problem where you have two interacting levels where you start in the infinite past in one of the states and then you linearly sweep the energy separation between the two levels and they come together forming an anti-crossing with gap delta and then linearly goes away again. And the problem is what is the transition probability? So if you start in the blue states, what's the probability that it remains in the blue states at the end of the sweep? And I can't use a laser here. So this problem has a simple solution in the coherent limit that the transition probability is given by this exponential of this factor of delta squared over V where delta is a minimum gap or the tunneling amplitude and V is a sweep rate. And this problem is relevant for a wide range of physical phenomenon including atomic collisions, chemical reactions, molecular magnets and of course quantum annealing. And physical realizations of the london zener problem are always affected by dissipation or coupling to the environment and there have been a broad interest on theoretical modeling of the dissipative london zener problems and I have just listed some of the more prominent references here. So what this problem has to do with quantum annealing exactly? So in quantum annealing we would like, or at least in the conventional quantum annealing, we would like to have an adiabatic evolution so that the system stays in the ground state and eventually ends up in the low energy state of an isenthermotonian which corresponds to a hard problem that we want to solve. And this is despite the systems going through some minimum gap in the middle of the evolution. And dissipation is an important factor in determining the success probability or the probability that the system can remain in the ground state. So in the weight coupling limit there's a trade-off between adiabaticity and thermal excitations in that if you go too fast, if you go too slow you are adiabatic, but thermal excitations can bring you out of the ground state and if you go too fast you end up having non-adiabatic transitions out of the ground state as well. And in the strong system bath coupling limit there have also studies shown that tunneling occurs between entangled system and bath states instead of just the system energy eigenstates. So that also complicates the situation. And also that there's very limited exploration in the intermediate coupling range. And we believe that doing this dissipative Landau-Zehner transition measurements, although it's a two-level problem it can shed lights in understanding the evolution of a large system of annealer during the small gap evolution. So we perform our measurements on a superconducting flux qubit which is one of the most common building blocks for quantum annealers. And it has a qubit Hamiltonian that has this epsilon sigma z and delta sigma x. So these two coefficients epsilon and delta are controlled by two external flux biases on the qubits which we call sigma z and sigma x. And if you look at the two-level pictures that represent the potential energy of the flux qubit you can see that phi z controls the tilt between the two wells. So that controls epsilon and phi x controls the tunneling barrier between the two states. So that controls a delta term. And there have been previous Landau-Zehner measurements in flux qubits. So in 2005 the MIT team performed Landau-Zehner-Struckeberg interference, which is basically measuring the steady state population after repeatedly going through the Landau-Zehner transitions. And they've incorporated a decoherence effect using some phenomenological T2 parameter. And in 2009 DOAPE group also performed a single passage Landau-Zehner transition. And they found that their data agrees with a strong coupling model which is the MRT theory, Microscopic Resonant Tunneling. And interestingly they found that using their data and this model shows that in this strong coupling limit the transition rate is actually the same as a coherent Landau-Zehner transition rate. Okay so our experimental setup to control the qubit we have a DC current as coupled to the x flux of the qubit that allows us to set the tunneling amplitude delta and we have a DC and a fast AWG combined to control the z flux. So that allows us to sweep the z flux with different time scales. And we also have a capacitively coupled microwave signal to do spectroscopy and coherence measurement on the qubit. And to read out the qubit state we use a transmission measurement through a flux sensitive resonator. That's this blue circuit here. And the measurement protocol is pretty simple. We prepare the qubit ground state in the far left of the symmetry point at time zero and then we linearly sweep phi z from phi z initial to phi z final with time tLz. And then we just measure the state populations in the end. So first we want to look at the transition probability in the short time scales where we expect the system to be coherent. So we show the final excited state probabilities as a function of tLz also for various phi x. And as expected, you can see that with increasing tLz, P e decreases exponentially. And that's in line with the prediction of the coherent Landau-Zener formula. So we fit the Landau-Zener formula to the measurement data and that allows us to extract an effective gap parameter delta Lz. And we can compare the delta measured by the Landau-Zener transition with our circuit model that's shown on the plot on the right. The orange dots are the depth measured by the Landau-Zener transition. And the circuit model is obtained by fitting to the spectroscopy measurement. That's the green triangles here. And we see a very good agreement between the circuit model and delta Lz. And just want to highlight that this agreement is quite remarkable because the circuit model is only fitted to spectroscopy data which is at around a few gigahertz for the qubit transition frequency. And we found that this model extrapolates, even when extrapolating to like tens of megahertz, it still agrees with the Landau-Zener measured minimum gap delta. So after confirming the behavior at short time scales, we look at the full time range that we have measured. So here I'm showing the final ground state probability as a function of T Lz plotted in log scale and for different phi x. And we can see that for large phi x corresponding to large minimum gap corresponds to this orange curve here. We have a non-monotonic dependence of the final ground state probability with respect to the sweep time T Lz. And this is in line with a competition between adiapaticity in the short time scale and thermalization near the gap in the intermediate time scale and thermal relaxation at the end of the sweep in the long. Long time scale. However, at a small gap or a small phi x, let's look at this greenish curve on the right here. We see that the behavior is quite different. PG increases monotonically and it's quite close to the coherent limit. And as a result of this, we also see that PG curves for different phi x actually crosses at some large sweep time. And what this means is that if a sweep time is large enough, you actually get a higher ground state probability when the minimum gap is smaller. This is quite counterintuitive. So next, I'll discuss our open system models to try to understand the data. We consider a qubit couple to the z flux noise given in this form hqb here. The flux noise operator q, it couples to the qubit sigma z operator with a proportionality constant of IP, which is a persistent current of the qubit. And we consider a combination of 1 over f and omit noise spectrum for the flux noise, which is verified and measured by many previous experiments on flux noise. And finally, we deduce the noise amplitude parameters based on our coherence measurements or T1 and T2 as a function of flux biases. So first, we consider a weak coupling to the environment, which can be modeled by the adiabatic master equation. In this limit, the environment acts as a perturbation leading to thermal transitions between energy eigenstates. So we can see that at large phi x, it predicts this non-monotonic dependence of Pg on Tlz, which agrees with our experiment data. But at small phi x, it almost plateaued near 0.5, which shows that this weak coupling limit does break down when the minimum gap is small. Next, we consider the strong coupling limit, which we model using the polar and transformed master equation. In this model, the effect of 1 over f noise is given in terms of this MRT parameters, the MRT width w and reorganization energy epsilon p, which are given in terms of the integrals of the noise spectrum. And in this model, the environment addresses the persistent current states. And so system energy eigenstate just no longer describes a system animal, and your tunneling delta becomes a perturbation parameter. And you see that its prediction agrees with our measurement data in the small phi x limit, but not in the large phi x limit. Finally, we can also compare the data and the two models, AME and PDRE, by plotting our results versus its dimensionless time tau. And we can observe some additional features, which is that whether in the AME or the PDRE model, we see these different curves for different phi x almost collapsed at long times. Whereas in our data, it kind of interpolates the AME result in the large phi x limit to the PDRE result in the small phi x limit. Okay, so just to summarize, we saw that when the evolution time TLZ is small, the measured transition probabilities are close to the coherent limit, and this is independent of the gap size of the problem. And then in the large gap limit, there's a non-monotonic dependence on the ground state probability on TLZ, consistent with weight coupling limit results that has been studied by previous literatures. And in the small gap limit, PG becomes monotonic, which is also consistent with strong coupling to low frequency noise. And just to highlight that the peculiar feature is that the crossing of different PG curves for different phi x, and you end up having higher ground state probability when the gap is smaller at long evolution times. Okay, I think I have, I'll just have our look slides here. I guess I can leave it here. So let's thank our speaker. Questions? I just want to say I want to acknowledge our funding agencies as well as our collaborators in the QEO program where we have many helpful discussions on experiments. Thanks for the nice review of the data. If you went to a qubit that had smaller circulating currents, so kind of less coupling to flux noise, how would this data change? I guess it would be more towards the weak coupling limit or just maybe, I shouldn't speculate, you can tell me. So what I expect based on the trend is that you still have a transition from weak to strong coupling, but that happens at a smaller minimum gap. So here you can see that the transition happens at around like say, it's about 50 megahertz or so, and that corresponds to the W, the MRT with more or less. So if you have 10 times smaller persistent current, your weak coupling limit will stay longer, so it can go around 5 megahertz and still remains weak coupling, my expectation. Other questions? Okay, if not, let's thank the speaker again and we go for a coffee.