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Chaotic oscillation and random-number generation based on nanoscale optical-energy transfer.

Naruse M, Kim SJ, Aono M, Hori H, Ohtsu M - Sci Rep (2014)

Bottom Line: Moreover, by evaluating the time-domain signals by statistical-test suites, we confirm that the signals are sufficiently random to qualify the system as a random-number generator (RNG).This study reveals that even relatively simple nanodevices that interact locally with each other through optical energy transfer at scales far below the wavelength of irradiating light can exhibit complex oscillatory dynamics.These findings are significant for applications such as ultrasmall RNGs.

View Article: PubMed Central - PubMed

Affiliation: Photonic Network Research Institute, National Institute of Information and Communications Technology, 4-2-1 Nukui-kita, Koganei, Tokyo 184-8795, Japan.

ABSTRACT
By using nanoscale energy-transfer dynamics and density matrix formalism, we demonstrate theoretically and numerically that chaotic oscillation and random-number generation occur in a nanoscale system. The physical system consists of a pair of quantum dots (QDs), with one QD smaller than the other, between which energy transfers via optical near-field interactions. When the system is pumped by continuous-wave radiation and incorporates a timing delay between two energy transfers within the system, it emits optical pulses. We refer to such QD pairs as nano-optical pulsers (NOPs). Irradiating an NOP with external periodic optical pulses causes the oscillating frequency of the NOP to synchronize with the external stimulus. We find that chaotic oscillation occurs in the NOP population when they are connected by an external time delay. Moreover, by evaluating the time-domain signals by statistical-test suites, we confirm that the signals are sufficiently random to qualify the system as a random-number generator (RNG). This study reveals that even relatively simple nanodevices that interact locally with each other through optical energy transfer at scales far below the wavelength of irradiating light can exhibit complex oscillatory dynamics. These findings are significant for applications such as ultrasmall RNGs.

No MeSH data available.


Related in: MedlinePlus

Chaos and random-number generation in nanosized system.(a) Lyapunov exponents as a function of control parameter αC. We used the following FET1 parameters, dimension = 7, delay = 10, evolve = 1, Scalemin = 10−5, and Scalemax = 0.7. The Lyapunov exponent λ ≤ 0 indicates no chaos. The dotted line shows λ = 0 (b) Analysis of properties of random numbers based on the improved FIPS test. (c) Schematic of cases that pass the improved FIPS test. For all 35 cases that pass the improved FIPS test, the corresponding Lyapunov exponent is positive [see panel (a)].
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f4: Chaos and random-number generation in nanosized system.(a) Lyapunov exponents as a function of control parameter αC. We used the following FET1 parameters, dimension = 7, delay = 10, evolve = 1, Scalemin = 10−5, and Scalemax = 0.7. The Lyapunov exponent λ ≤ 0 indicates no chaos. The dotted line shows λ = 0 (b) Analysis of properties of random numbers based on the improved FIPS test. (c) Schematic of cases that pass the improved FIPS test. For all 35 cases that pass the improved FIPS test, the corresponding Lyapunov exponent is positive [see panel (a)].

Mentions: Another criterion satisfied by chaos is expressed by the maximal Lyapunov exponent (MLE)2223. Suppose that a trajectory exhibits chaotic behavior, which means that the final difference between two trajectories with a subtle initial difference δZ0 grows exponentially. In other words, . The MLE is defined by where λ ≤ 0 indicates no chaos2022. We used the FET1 code developed by Wolf et al.38 to estimate the MLE from a time series. Figure 4a shows the calculated MLE as a function of the control parameter αC. The results show that, for instance, λ is positive for 0.0148 < αC < 0.0225. This particular range coincides with the range over which chaos occurs in the local maxima and minima (Fig. 3b). Also, for the 78 points in this particular regime, there are 26 points that satisfy the random-number conditions discussed below. This result clearly indicates that the physics of near-field optics allows for chaotic phenomena.


Chaotic oscillation and random-number generation based on nanoscale optical-energy transfer.

Naruse M, Kim SJ, Aono M, Hori H, Ohtsu M - Sci Rep (2014)

Chaos and random-number generation in nanosized system.(a) Lyapunov exponents as a function of control parameter αC. We used the following FET1 parameters, dimension = 7, delay = 10, evolve = 1, Scalemin = 10−5, and Scalemax = 0.7. The Lyapunov exponent λ ≤ 0 indicates no chaos. The dotted line shows λ = 0 (b) Analysis of properties of random numbers based on the improved FIPS test. (c) Schematic of cases that pass the improved FIPS test. For all 35 cases that pass the improved FIPS test, the corresponding Lyapunov exponent is positive [see panel (a)].
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4129418&req=5

f4: Chaos and random-number generation in nanosized system.(a) Lyapunov exponents as a function of control parameter αC. We used the following FET1 parameters, dimension = 7, delay = 10, evolve = 1, Scalemin = 10−5, and Scalemax = 0.7. The Lyapunov exponent λ ≤ 0 indicates no chaos. The dotted line shows λ = 0 (b) Analysis of properties of random numbers based on the improved FIPS test. (c) Schematic of cases that pass the improved FIPS test. For all 35 cases that pass the improved FIPS test, the corresponding Lyapunov exponent is positive [see panel (a)].
Mentions: Another criterion satisfied by chaos is expressed by the maximal Lyapunov exponent (MLE)2223. Suppose that a trajectory exhibits chaotic behavior, which means that the final difference between two trajectories with a subtle initial difference δZ0 grows exponentially. In other words, . The MLE is defined by where λ ≤ 0 indicates no chaos2022. We used the FET1 code developed by Wolf et al.38 to estimate the MLE from a time series. Figure 4a shows the calculated MLE as a function of the control parameter αC. The results show that, for instance, λ is positive for 0.0148 < αC < 0.0225. This particular range coincides with the range over which chaos occurs in the local maxima and minima (Fig. 3b). Also, for the 78 points in this particular regime, there are 26 points that satisfy the random-number conditions discussed below. This result clearly indicates that the physics of near-field optics allows for chaotic phenomena.

Bottom Line: Moreover, by evaluating the time-domain signals by statistical-test suites, we confirm that the signals are sufficiently random to qualify the system as a random-number generator (RNG).This study reveals that even relatively simple nanodevices that interact locally with each other through optical energy transfer at scales far below the wavelength of irradiating light can exhibit complex oscillatory dynamics.These findings are significant for applications such as ultrasmall RNGs.

View Article: PubMed Central - PubMed

Affiliation: Photonic Network Research Institute, National Institute of Information and Communications Technology, 4-2-1 Nukui-kita, Koganei, Tokyo 184-8795, Japan.

ABSTRACT
By using nanoscale energy-transfer dynamics and density matrix formalism, we demonstrate theoretically and numerically that chaotic oscillation and random-number generation occur in a nanoscale system. The physical system consists of a pair of quantum dots (QDs), with one QD smaller than the other, between which energy transfers via optical near-field interactions. When the system is pumped by continuous-wave radiation and incorporates a timing delay between two energy transfers within the system, it emits optical pulses. We refer to such QD pairs as nano-optical pulsers (NOPs). Irradiating an NOP with external periodic optical pulses causes the oscillating frequency of the NOP to synchronize with the external stimulus. We find that chaotic oscillation occurs in the NOP population when they are connected by an external time delay. Moreover, by evaluating the time-domain signals by statistical-test suites, we confirm that the signals are sufficiently random to qualify the system as a random-number generator (RNG). This study reveals that even relatively simple nanodevices that interact locally with each other through optical energy transfer at scales far below the wavelength of irradiating light can exhibit complex oscillatory dynamics. These findings are significant for applications such as ultrasmall RNGs.

No MeSH data available.


Related in: MedlinePlus