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Physical Review A

Application of harmonic and anharmonic frequency crystals for manipulation with quantum states

R. N. Shakhmuratov

Published Oct 29, 2018• 1 citation
Publisher

Abstract

Filtering of weak pulses through a medium with infinite periodic structure in the absorption and/or transmission spectrum is analyzed. Two types of filters are considered. The first, named harmonic frequency crystal (HFC), is the filter whose periodic structure is harmonic and described by the sine or cosine function of frequency with the fundamental period. The second, named anharmonic frequency crystal (AHFC), also has a periodic structure with one fundamental period but it is described by the function containing many harmonics of the fundamental period. AHFC demonstrates properties quite similar to those of a high-finesse atomic frequency comb (AFC) with a limited number of absorption peaks separated by transparency windows. Filtering of the pulse through AHFC produces a prompt pulse accompanied by a few delayed pulses. Time spacing $T$ of the delayed pulses is inversely proportional to the comb period. On the contrary, HFC transforms the input pulse into a train of many delayed pulses, generated at times $nT$, where $n$ is an integer. Maximum amplitudes of the delayed pulses follow a wide bell-shaped envelope. Both HFC and AHFC are extensions of AFC, which was proposed to implement quantum memory protocols for single photons. In this paper, it is proposed to create time-bin qubits with the help of a short pulse filtering through HFC. HFC is also proposed to implement tomography of these quantum states. Another promising application of HFC is the optical detection of ultrasound in biological tissues for ultrasound-modulated optical tomography. Since HFC allows one to generate pulses with longer delay with respect to the excitation pulse, one could obtain higher discrimination between weak acoustically generated sidebands and the carrier.

DOI
10.1103/physreva.98.043851

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Filtering of weak pulses through a medium with infinite periodic structure in the absorption and/or transmission spectrum is analyzed. Two types of filters are considered. The first, named harmonic frequency crystal (HFC), is the filter whose periodic structure is harmonic and described by the sine or cosine function of frequency with the fundamental period. The second, named anharmonic frequency crystal (AHFC), also has a periodic structure with one fundamental period but it is described by the function containing many harmonics of the fundamental period. AHFC demonstrates properties quite similar to those of a high-finesse atomic frequency comb (AFC) with a limited number of absorption peaks separated by transparency windows. Filtering of the pulse through AHFC produces a prompt pulse accompanied by a few delayed pulses. Time spacing TTT of the delayed pulses is inversely proportional to the comb period. On the contrary, HFC transforms the input pulse into a train of many delayed pulses, generated at times nTnTnT, where nnn is an integer. Maximum amplitudes of the delayed pulses follow a wide bell-shaped envelope. Both HFC and AHFC are extensions of AFC, which was proposed to implement quantum memory protocols for single photons. In this paper, it is proposed to create time-bin qubits with the help of a short pulse filtering through HFC. HFC is also proposed to implement tomography of these quantum states. Another promising application of HFC is the optical detection of ultrasound in biological tissues for ultrasound-modulated optical tomography. Since HFC allows one to generate pulses with longer delay with respect to the excitation pulse, one could obtain higher discrimination between weak acoustically generated sidebands and the carrier.
Pulse filtering through a medium with infinite periodic structure in transmission spectrum is analyzed. Two types of filters are considered. The first, named harmonic frequency crystal (HFC), is the filter whose widths of transmitting and absorbing windows are equal. The second, named anharmonic frequency crystal (AHFC), has narrow absorption peaks separated by wide transmission windows. AHFC of moderate optical thickness demonstrates properties quite similar to those of high finesse atomic frequency comb (AFC) with limited number of the absorption peaks, which produce a few pulses from a short input pulse. On the contrary, HFC transforms the input pulse into a train of pulses whose maximum amplitudes follow a wide bell-shaped envelope. HFC allows to find an exact universal analytical solution, which describes transformation of a broadband pulse into a train of short pulses, slow light propagation for a pulse whose spectral width fits one of the transparency windows of the crystal, and absorption typical for a single line absorber if the pulse spectrum falls into one of the absorption peaks. Potential applications of HFC are discussed.
Abstract A protocol, which essentially increases the efficiency of the quantum memory based on the atomic frequency comb (AFC), is proposed. It is well known that a weak short pulse, transmitted trough a medium with a periodic structure of absorption peaks separated by transparency windows (AFC), is transformed into prompt and delayed pulses. Time delay is equal to the inverse value of the frequency period of the peaks. It is proposed to send the prompt pulse again through the medium and to make both delayed pulses to interfere. This leads to the essential increase of the efficiency of the AFC storage protocol close to 100%.
We present results of a novel and highly sensitive technique for the optical detection of ultrasound using the selective storage of frequency shifted photons in an inherently highly efficient and low noise atomic frequency comb (AFC) based quantum memory. The ultrasound ‘tagged’ optical sidebands are absorbed within a pair of symmetric AFCs, generated via optical pumping in a Pr3+:Y2SiO5 sample (tooth separation Δ = 150 kHz, comb finesse fc ~ 2 and optical depth αL ~ 2), separated by twice the ultrasound modulation frequency (1.5 MHz) and centered on either side of a broad spectral pit (1.7 MHz width) allowing transmission of the carrier. The stored sidebands are recovered with 10-20% efficiency as a photon echo (as defined by the comb parameters), and we demonstrate a record 49 dB discrimination between the sidebands and the carrier pulse, high discrimination being important for imaging tissues at depth. We further demonstrate detector limited discrimination (~29 dB) using a highly scattered beam, confirming that the technique is immune to speckle decorrelation. We show that it also remains valid in the case of optically thin samples, and thus represents a significant improvement over other ultrasound detection methods based on rare-earth-ion-doped crystals. These results strongly suggest the suitability of our technique for high-resolution non-contact real-time imaging of biological tissues.
The interaction of ultrasound and light in biological tissues results in a small amount of the scattered light being shifted relative to the carrier frequency (typically 1 part in 108). We have developed an inherently efficient and low noise quantum memory based technique to selectively absorb these ‘ultrasound tagged’ photons in a pair of atomic frequency combs, and recover them delayed in time as a photon echo. In this manner we have demonstrated record ultrasoundmodulated sideband-to-carrier discrimination (49dB). Further, we confirm that the technique is compatible with highly scattering samples, and present initial acoustic pulse tracking measurements. This strongly suggests the suitability of the technique for biological tissue imaging.
Quantum memories are inherently highly efficient and display low noise, making them particularly suitable for the optical detection of ultrasound. Here, we use an atomic-frequency-comb based quantum memory to demonstrate sensitive ultrasound detection, realising a 49 dB discrimination between the sidebands and the carrier. The method remains valid in the case of optically thin samples and thus represents a significant improvement over other ultrasound detection methods based on rare-earth-ion-doped crystals. Furthermore, we show that this non-destructive non-contact approach is also compatible with highly scattering samples and suggest its particular suitability for the real-time imaging of biological tissues.
Faithful storage and coherent manipulation of quantum optical pulses are key for long distance quantum communications and quantum computing. Combining these functions in a light–matter interface that can be integrated on-chip with other photonic quantum technologies, e.g. sources of entangled photons, is an important step towards these applications. To date there have only been a few demonstrations of coherent pulse manipulation utilizing optical storage devices compatible with quantum states, and that only in atomic gas media (making integration difficult) and with limited capabilities. Here we describe how a broadband waveguide quantum memory based on the atomic frequency comb (AFC) protocol can be used as a programmable processor for essentially arbitrary spectral and temporal manipulations of individual quantum optical pulses. Using weak coherent optical pulses at the few photon level, we experimentally demonstrate sequencing, time-to-frequency multiplexing and demultiplexing, splitting, interfering, temporal and spectral filtering, compressing and stretching as well as selective delaying. Our integrated light–matter interface offers high-rate, robust and easily configurable manipulation of quantum optical pulses and brings fully practical optical quantum devices one step closer to reality. Furthermore, as the AFC protocol is suitable for storage of intense light pulses, our processor may also find applications in classical communications.