Quantum feedback cooling of a single trapped ion in front of a mirror

Steixner, Viktor; Rabl, Peter; Zoller, P.

doi:10.1103/physreva.72.043826

Cited by 38 publications

(33 citation statements)

References 32 publications

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“…Continuous measurement has become increasingly important in the last decade, due mainly to the growing interest in the application of feedback control in quantum systems [1,2,3,4,5,6,7,8,9,10,11]. In feedback control a system is continuously measured, and this information is used while the measurement proceeds (that is, in real time) to modify the system Hamiltonian so as to obtain some desired behavior.…”

Section: Introductionmentioning

confidence: 99%

A straightforward introduction to continuous quantum measurement

Jacobs¹,

Steck

2006

Contemporary Physics

517

594

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We present a pedagogical treatment of the formalism of continuous quantum measurement. Our aim is to show the reader how the equations describing such measurements are derived and manipulated in a direct manner. We also give elementary background material for those new to measurement theory, and describe further various aspects of continuous measurements that should be helpful to those wanting to use such measurements in applications. Specifically, we use the simple and direct approach of generalized measurements to derive the stochastic master equation describing the continuous measurements of observables, give a tutorial on stochastic calculus, treat multiple observers and inefficient detection, examine a general form of the measurement master equation, and show how the master equation leads to information gain and disturbance. To conclude, we give a detailed treatment of imaging the resonance fluorescence from a single atom as a concrete example of how a continuous position measurement arises in a physical system.

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Section: Introductionmentioning

confidence: 99%

A straightforward introduction to continuous quantum measurement

Jacobs¹,

Steck

2006

Contemporary Physics

517

594

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“…As shown below, in our model the incorporation of quantum feedback competing with laser cooling predicts such behavior, i.e., the existence of an optimal gain for maximal cooling (for a detailed description cf. [23]). …”

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“…As it is impractical to keep track of the whole photocurrent in the experiment, we derive a master equation for the density operator averaged over all possible realisation of I c (t), µ(t). Along the ways of the Wiseman-Milburn theory of quantum feedback [12], for a phase shift of (−π/2), we obtain the quantum feedback master equation [23] …”

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confidence: 99%

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Feedback Cooling of a Single Trapped Ion

et al. 2006

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Based on a real-time measurement of the motion of a single ion in a Paul trap, we demonstrate its electro-mechanical cooling below the Doppler limit by homodyne feedback control (cold damping). The feedback cooling results are well described by a model based on a quantum mechanical Master Equation.PACS numbers: 3.65. Ta, 42.50.Lc 32.80.Pj, 42.50.Ct, 42.50.Vk, 32.80.Lg Quantum optics, and more recently mesoscopic condensed matter physics, have taken a leading role in realizing individual quantum systems, which can be monitored continuously in quantum limited measurements, and at the same time can be controlled by external fields on time scales fast in comparison with the system evolution. Examples include cold trapped ions and atoms [1], cavity QED [2,3,4,5] and nanomechanical systems [6]. This setting opens the possibility of manipulating individual quantum systems by feedback, a problem which is not only of a fundamental interest in quantum mechanics, but also promises a new route to generating interesting quantum states in the laboratory. First experimental efforts to realize quantum feedback have been reported only recently. While not all of them may qualify as quantum feedback in a strict sense, feedback has been applied to various quantum systems [5,7,8,9,10,11]. On the theory side, this has motivated during the last decade the development of a quantum feedback theory [12,13], where the basic ingredients are the interplay between quantum dynamics and the back-action of the measurement on the system evolution. In this letter we report a first experiment to demonstrate quantum feedback control, i.e. quantum feedback cooling, of a single trapped ion by monitoring the fluorescence of the laser driven ion in front of a mirror. We establish a continuous measurement of the position of the ion which allows us to act back in a feedback loop demonstrating "cold damping" [14,15]. We will show that quantum control theory based on a quantum optical modelling of the system dynamics and continuous measurement theory of photodetection provides a quantitative understanding of the experimental results.We study a single 138 Ba + ion in a miniature Paul trap which is continuously laser-excited and laser-cooled to the Doppler limit on its S 1/2 to P 1/2 transition at 493 nm, as outlined in Fig. 1. The ion is driven by a laser near the atomic resonance, and the scattered light is emitted both into the radiation modes reflected by the mirror, as well as the other (background) modes of the quantized light field [16]. Light scattered into the mirror modes can either reach the photodetector directly, or after reflection from the mirror. From the resulting interference the motion of the ion (its projection onto the ion-mirror axis) is detected as a vibrational sideband in the fluctuation spectrum of the photon counting signal [17]. Of the three sidebands at about (1,1.2,2.3) MHz, corresponding to the three axes of vibration, we observe the one at ν = 1 MHz. It has a width Γ ≈ 400 Hz and is superimposed on the background shot noise...

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“…This is the same feature which underlies recent studies of electromagnetically induced transparency, slow light in atomic gases and quantum memory of light in atomic ensembles. The present setup of dispersive readout of the atomic velocity complements and is in contrast to ongoing experiments of quantum feedback cooling of a single two-level ion in front of a mirror [14,15], where the position of the ion is continuously monitored by emission of light into the mirror mode, as analyzed theoretically in our recent publication [16].…”

Section: Introductionmentioning

confidence: 99%

Quantum-limited velocity readout and quantum feedback cooling of a trapped ion via electromagnetically induced transparency

2005

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We discuss continuous observation of the momentum of a single atom by employing the high velocity sensitivity of the index of refraction in a driven Λ-system based on electromagnetically induced transparency (EIT). In the ideal limit of unit collection efficiency this provides a quantum limited measurement with minimal backaction on the atomic motion. A feedback loop, which drives the atom with a force proportional to measured signal, provides a cooling mechanism for the atomic motion. We derive the master equation which describes the feedback cooling and show that in the Lamb-Dicke limit the steady state energies are close to the ground state, limited only by the photon collection efficiency. Outside of the Lamb-Dicke regime the predicted temperatures are well below the Doppler limit.

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Quantum feedback cooling of a single trapped ion in front of a mirror

Cited by 38 publications

References 32 publications

A straightforward introduction to continuous quantum measurement

A straightforward introduction to continuous quantum measurement

Feedback Cooling of a Single Trapped Ion

Quantum-limited velocity readout and quantum feedback cooling of a trapped ion via electromagnetically induced transparency

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