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arXiv:1209.0352 · New Journal of Physics

Analysis of a photon number resolving detector based on fluorescence readout of an ion Coulomb crystal quantum memory inside an optical cavity

Christoph Clausen, Nicolas Sangouard, Michael Drewsen

Published Feb 14, 2013• 13 citations
arXivHTMLPDF

Abstract

The ability to detect single photons with a high efficiency is a crucial requirement for various quantum information applications. By combining the storage process of a quantum memory for photons with fluorescence-based quantum state measurement, it is, in principle, possible to achieve high-efficiency photon counting in large ensembles of atoms. The large number of atoms can, however, pose significant problems in terms of noise stemming from imperfect initial state preparation and off-resonant fluorescence. We identify and analyse a concrete implementation of a photon number resolving detector based on an ion Coulomb crystal inside a moderately high-finesse optical cavity. The cavity enhancement leads to an effective optical depth of 15 for a finesse of 3000 with only about 1500 ions interacting with the light field. We show that these values allow for essentially noiseless detection with an efficiency larger than 93%. Moderate experimental parameters allow for repetition rates of about 3 kHz, limited by the time needed for fluorescence collection and re-cooling of the ions between trials. Our analysis may lead to the first implementation of a photon number resolving detector in atomic ensembles.

DOI
10.1088/1367-2630/15/2/025021

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The ability to detect single photons with a high efficiency is a crucial requirement for various quantum information applications. By combining the storage process of a quantum memory for photons with fluorescence-based quantum state measurement, it is, in principle, possible to achieve high-efficiency photon counting in large ensembles of atoms. The large number of atoms can, however, pose significant problems in terms of noise stemming from imperfect initial state preparation and off-resonant fluorescence. We identify and analyse a concrete implementation of a photon number resolving detector based on an ion Coulomb crystal inside a moderately high-finesse optical cavity. The cavity enhancement leads to an effective optical depth of 15 for a finesse of 3000 with only about 1500 ions interacting with the light field. We show that these values allow for essentially noiseless detection with an efficiency larger than 93%. Moderate experimental parameters allow for repetition rates of about 3 kHz, limited by the time needed for fluorescence collection and re-cooling of the ions between trials. Our analysis may lead to the first implementation of a photon number resolving detector in atomic ensembles.
We study the atom-vapor-based photon-number-resolving detection from first principles, including quantum-mechanical treatment of the electromagnetic field. We study a photon detector model that combines coherently controlled absorption of light and resonance fluorescence to achieve photon counting at room temperature. In particular we identify the fundamental limits to this particular scheme of photon detection. We show that there exists a time-energy uncertainty between the incident pulse strength and the time period of the incident pulse. We verify the role of a large ensemble of atoms to boost the efficiency of such a detector.
Long-range transport of quantum information across a network is most readily achieved through the use of photons as the information carriers. The nodes of such a quantum network are most naturally a quantum memory or information processor, which typically do not rely upon photonic qubits. Realizing a large-scale distributed quantum network therefore requires an efficient interface between the two physical manifestations of the quantum information. The most promising platform for realizing a quantum computer is the manipulation of trapped atomic ions, as this system has demonstrated all the fundamental requirements to realize a quantum computer. Additionally, trapped ions posses long coherence times necessary for quantum memories. The interface between atomic and photonic qubits relies on a high photon emission rate into the collected solid angle. Most methods of photon collection for quantum networks use a high numerical aperture microscope objective, which only collects on the order of 1% of all the emitted photons. This results in a small probability of successfully linking two quantum nodes. In this work, I present the design, simulation, and implementation of a trapped ion cavity QED system capable of improving the photon collection efficiency. A single ytterbium ion is coupled to a high-finesse optical cavity. The photon scatter rate into the cavity mode is enhanced by a factor of 130 over the free-space scatter rate into the cavity solid angle. This represents the first step towards realizing a protocol to entangle the polarization of an emitted photon to the Zeeman sublevels of the ion with high photon collection efficiency. Simulations of the experimental system indicate that with an optical cavity up to 4% of the light emitted by the ion can be collected.
We propose a method that can, in principle, achieve nearly ideal photon counting, by combining the techniques of photonic quantum memory and ion-trap quantum-state measurements. After mapping the quantum state of a propagating light pulse onto metastable collective excitations of a trapped cold atomic gas, it is possible to monitor the resonance fluorescence induced by an additional laser field that couples only to the metastable excited state. Even with a photon collection/detection efficiency as low as 10%, it is possible to achieve photon counting with efficiency exceeding 99%.
This work is devoted to the development of novel photon-detector models at room temperature using quantum optics elements. This work comprises of two photon-number-resolving detector (PNRD) models, and the application of PNRD in LIDAR. The first model is based on using a two-mode squeezing device to resolve photon number at room temperature. In this model we study the average intensity-intensity correlations signal at the output of a two-mode squeezing device with |N> and |α> as the two input modes. We show that the input photon-number can be resolved from the average intensity-intensity correlations. In particular, we show jumps in the average intensity-intensity correlations signal as a function of input photon-number N. Therefore, we propose that such a device may be deployed as photon-number-resolving detector at room temperature with high efficiency. In the second model we study the atom-vapor based PNRD from first principles, including quantum mechanical treatment of the electromagnetic field. We analyze a photon detector model that combines coherently controlled absorption of light and resonance fluorescence to achieve photon counting at room temperature. In particular we identify the fundamental limits to this particular scheme of photon detection. We show that there exists a time-energy uncertainty between the incident pulse strength and the time period of the incident pulse. We verify the role of a large ensemble of atoms in boosting the efficiency of such a detector. Lastly, we show the application of PNRD technique to enhance laser range finding and light detection and ranging. We present a technique that improves the signal-to-noise-ratio (SNR) of range-finding, sensing, and other light-detection applications. The technique filters out low photon numbers using PNRD. This technique has no classical analog and cannot be achieved with classical detectors. We investigate the properties of our technique and show under what conditions the scheme surpasses the classical SNR. Finally, we simulate the operation of a rangefinder, showing improvement with a low number of signal samplings and confirming the theory with a high number of signal samplings.
Quantum memories, capable of storing single photons or other quantum states of light, to be retrieved on demand, offer a route to large-scale quantum information processing with light. A promising class of memories is based on far-off-resonant Raman absorption in ensembles of $\mathrm{\ensuremath{\Lambda}}$-type atoms. However, at room temperature these systems exhibit unwanted four-wave mixing, which is prohibitive for applications at the single-photon level. Here, we show how this noise can be suppressed by placing the storage medium inside a moderate-finesse optical cavity, thereby removing the main roadblock hindering this approach to quantum memory.
A detailed description and theoretical analysis of experiments achieving coherent coupling between an ion Coulomb crystal and an optical cavity field are presented. The various methods used to measure the coherent coupling rate between large ion Coulomb crystals in a linear quadrupole radiofrequency ion trap and a single-field mode of a moderately high-finesse cavity are described in detail. Theoretical models based on a semiclassical approach are applied in assessment of the experimental results of P. F. Herskind et al.[Nature Phys. 5, 494 (2009)] and of complementary new measurements. Generally, a very good agreement between theory and experiments is obtained.