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Register a new userEfficient sideband cooling protocol for long trapped-ion chains
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Trapped ions are a promising candidate for large scale quantum computation. Several systems have been built in both academic and industrial settings to implement modestly-sized quantum algorithms. Efficient cooling of the motional degrees of freedom is a key requirement for high-fidelity quantum operations using trapped ions. Here, we present a technique whereby individual ions are used to cool individual motional modes in parallel, reducing the time required to bring an ion chain to its motional ground state. We demonstrate this technique experimentally and develop a model to understand the efficiency of our parallel sideband cooling technique compared to more traditional methods. This technique is applicable to any system using resolved sideband cooling of co-trapped atomic species and only requires individual addressing of the trapped particles.
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We report a demonstration and quantitative characterization of one-dimensional cavity cooling of a single trapped 88Sr+ ion in the resolved sideband regime. We measure the spectrum of cavity transitions, the rates of cavity heating and cooling, and the steady-state cooling limit. The cavity cooling dynamics and cooling limit of 22.5(3) motional quanta, limited by the moderate coupling between the ion and the cavity, are consistent with a simple model [Phys. Rev. A 64, 033405] without any free parameters, validating the rate equation model for cavity cooling.
We study sympathetic cooling of the radial ion motion in a linear RF trap in mixed barium-ytterbium chains. Barium ions are Doppler-cooled, while ytterbium ions are cooled through their interaction with cold barium ions. We estimate the efficiency of sympathetic cooling by measuring the average occupation quantum numbers, and thus the temperature, of all radial normal modes of motion in the ion chain. The full set of orderings in a chain of two barium and two ytterbium ions have been probed, and we show that the average thermal occupation numbers for all chain configurations strongly depend on the trap aspect ratio. We demonstrate efficient sympathetic cooling of all radial normal modes for the trap aspect ratio of approximately 2.9.
Trapped ion in the Lamb-Dicke regime with the Lamb-Dicke parameter $etall1$ can be cooled down to its motional ground state using sideband cooling. Standard sideband cooling works in the weak sideband coupling limit, where the sideband coupling strength is small compared to the natural linewidth $gamma$ of the internal excited state, with a cooling rate much less than $gamma$. Here we consider cooling schemes in the strong sideband coupling regime, where the sideband coupling strength is comparable or even greater than $gamma$. We derive analytic expressions for the cooling rate and the average occupation of the motional steady state in this regime, based on which we show that one can reach a cooling rate which is proportional to $gamma$, while at the same time the steady state occupation increases by a correction term proportional to $eta^{2}$ compared to the weak sideband coupling limit. We demonstrate with numerical simulations that our analytic expressions faithfully recover the exact dynamics in the strong sideband coupling regime.
We demonstrate ground-state cooling of a trapped ion using radio-frequency (RF) radiation. This is a powerful tool for the implementation of quantum operations, where RF or microwave radiation instead of lasers is used for motional quantum state engineering. We measure a mean phonon number of $overline{n} = 0.13(4)$ after sideband cooling, corresponding to a ground-state occupation probability of 88(7)%. After preparing in the vibrational ground state, we demonstrate motional state engineering by driving Rabi oscillations between the n=0 and n=1 Fock states. We also use the ability to ground-state cool to accurately measure the motional heating rate and report a reduction by almost two orders of magnitude compared to our previously measured result, which we attribute to carefully eliminating sources of electrical noise in the system.
We study the formation and destabilization of dark states in a single trapped 88Sr+ ion caused by the cooling and repumping laser fields required for Doppler cooling and fluorescence detection of the ion. By numerically solving the time-dependent density matrix equations for the eight-level system consisting of the sublevels of the 5s 2S1/2, 5p 2P1/2, and 4d 2D3/2 states, we analyze the different types of dark states and how to prevent them in order to maximize the scattering rate, which is crucial for both the cooling and the detection of the ion. The influence of the laser linewidths and ion motion on the scattering rate and the dark resonances is studied. The calculations are then compared with experimental results obtained with an endcap ion trap system located at the National Research Council of Canada and found to be in good agreement. The results are applicable also to other alkaline earth ions and isotopes without hyperfine structure.
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