Intensity-Product-Based Optical Sensing to Beat the Diffraction Limit in an Interferometer.

The classically defined minimum uncertainty of the optical phase is known as the standard quantum limit or shot-noise limit (SNL), originating in the uncertainty principle of quantum mechanics. Based on the SNL, the phase sensitivity is inversely proportional to K, where K is the number of interfering photons or statistically measured events. Thus, using a high-power laser is advantageous to enhance sensitivity due to the K gain in the signal-to-noise ratio. In a typical interferometer, however, the resolution remains in the diffraction limit of the K = 1 case unless the interfering photons are resolved as in quantum sensing. Here, a projection measurement method in quantum sensing is adapted for classical sensing to achieve an additional K gain in the resolution. To understand the projection measurements, several types of conventional interferometers based on N-wave interference are coherently analyzed as a classical reference and numerically compared with the proposed method. As a result, the Kth-order intensity product applied to the N-wave spectrometer exceeds the diffraction limit in classical sensing and the Heisenberg limit in quantum sensing, where the classical N-slit system inherently satisfies the Heisenberg limit of π/N in resolution.

A Quantum Ring Laser Gyroscope Based on Coherence de Broglie Waves.

In sensors, the highest precision in measurements is given by vacuum fluctuations of quantum mechanics, resulting in a shot noise limit. In a Mach-Zenhder interferometer (MZI), the intensity measurement is correlated with the phase, and thus, the precision measurement (Δn) is coupled with the phase resolution (Δφ) by the Heisenberg uncertainty principle. Quantum metrology offers a different solution to this precision measurement using nonclassical light such as squeezed light or higher-order entangled-photon pairs, resulting in a smaller Δφ and sub-shot noise limit. Here, we propose another method for the high precision measurement overcoming the diffraction limit in classical physics, where the smaller Δφ is achieved by phase quantization in a coupled interferometric system of coherence de Broglie waves. For a potential application of the proposed method, a quantum ring laser gyroscope is presented as a quantum version of the conventional ring laser gyroscope used for inertial navigation and geodesy.

Analysis of Imperfect Rephasing in Photon Echo-Based Quantum Memories.

Over the last two decades, quantum memories have been intensively studied for potential applications of quantum repeaters in quantum networks. Various protocols have also been developed. To satisfy no noise echoes caused by spontaneous emission processes, a conventional two-pulse photon-echo scheme has been modified. The resulting methods include double-rephasing, ac Stark, dc Stark, controlled echo, and atomic frequency comb methods. In these methods, the main purpose of modification is to remove any chance of a population residual on the excited state during the rephasing process. Here, we investigate a typical Gaussian rephasing pulse-based double-rephasing photon-echo scheme. For a complete understanding of the coherence leakage by the Gaussian pulse itself, ensemble atoms are thoroughly investigated for all temporal components of the Gaussian pulse, whose maximum echo efficiency is 26% in amplitude, which is unacceptable for quantum memory applications.

Understanding of Collective Atom Phase Control in Modified Photon Echoes for a Near-Perfect Storage Time-Extended Quantum Memory.

A near-perfect storage time-extended photon echo-based quantum memory protocol has been analyzed by solving the Maxwell-Bloch equations for a backward scheme in a three-level system. The backward photon echo scheme is combined with a controlled coherence conversion process via controlled Rabi flopping to a third state, where the control Rabi flopping collectively shifts the phase of the ensemble coherence. The propagation direction of photon echoes is coherently determined by the phase-matching condition between the data (quantum) and the control (classical) pulses. Herein, we discuss the classical controllability of a quantum state for both phase and propagation direction by manipulating the control pulses in both single and double rephasing photon echo schemes of a three-level system. Compared with the well-understood uses of two-level photon echoes, the Maxwell-Bloch equations for a three-level system have a critical limitation regarding the phase change when interacting with an arbitrary control pulse area.

Analysis of Controlled Rabi Flopping in a Double Rephasing Photon Echo Scheme for Quantum Memories.

A double rephasing scheme of a photon echo is analyzed for inversion-free photon echo-based quantum memories using controlled Rabi flopping, where the Rabi flopping is used for phase control of collective atom coherence. Unlike the rephasing-caused π-phase shift in a single rephasing scheme, the control Rabi flopping between the excited state and an auxiliary third state induces coherence inversion. Thus, the absorptive photon echo in a double rephasing scheme can be manipulated to be emissive. Here, we present a quantum coherence control of atom phases in a double rephasing photon echo scheme for emissive photon echoes for quantum memory applications.

Phase-controlled coherent photons for the quantum correlations in a delayed-choice quantum eraser scheme.

The delayed-choice quantum eraser has been intensively studied for the wave-particle duality of a single photon in an interferometric system over the last decades. Super-resolution has been studied over decades for quantum sensing to overcome the standard quantum limit. For the super-resolution, either quantum features of higher-order entangled photon pairs or classical features of phase-controlled coherent photons have been successfully demonstrated. Here, a method of classically excited super-resolution is presented for the phase-controlled coherent photons in a quarter-wave plate-modified quantum eraser scheme. To support the underlying physics of the super-resolution, nonlocal correlation is also presented with an additional frequency-polarization basis control via selective product-basis measurements.

Coherently excited superresolution using intensity product of phase-controlled quantum erasers via polarization-basis projection measurements.

Recently, the delayed-choice quantum eraser has been applied for coherently excited superresolution using phase-controlled projection measurements of laser light to overcome the diffraction limit in classical physics as well as to solve the limited order N of the N00N state in quantum physics. Here, a general scheme of the phase-controlled quantum eraser-based superresolution is proposed for quantum sensing satisfying the Heisenberg limit, and its general solution is derived for an arbitrary Nth-order intensity correlation. Furthermore, phase quantization of the proposed superresolution is discussed to better understand the wave nature of quantum mechanics. Unlike other methods of superresolution in quantum sensing, the proposed method is for the intensity products between phase-controlled quantum erasers and thus is compatible with most conventional sensing metrologies.

Coherently driven quantum features using a linear optics-based polarization-basis control.

Quantum entanglement generation is generally known to be impossible by any classical means. According to Poisson statistics, coherent photons are not considered quantum particles due to the bunching phenomenon. Recently, a coherence approach has been applied for quantum correlations such as the Hong-Ou-Mandel (HOM) effect, Franson-type nonlocal correlation, and delayed-choice quantum eraser to understand the mysterious quantum features. In the coherence approach, the quantum correlation has been now understood as a direct result of selective measurements between product bases of phase-coherent photons. Especially in the HOM interpretation, it has been understood that a fixed sum-phase relation between paired photons is the bedrock of quantum entanglement. Here, a coherently excited HOM model is proposed, analyzed, and discussed for the fundamental physics of two-photon correlation using linear optics-based polarization-basis control. For this, polarization-frequency correlation in a Mach-Zehnder interferometer is coherently excited using synchronized acousto-optic modulators, where polarization-basis control is conducted via a selective measurement process of the heterodyne signals. Like quantum operator-based destructive interference in the HOM theory, a perfectly coherent analysis shows the same HOM effects of the paired coherent photons on a beam splitter, whereas individual output intensities are uniform.

Observations of the delayed-choice quantum eraser using coherent photons.

Quantum superposition is the cornerstone of quantum mechanics, where interference fringes originate in the self-interference of a single photon via indistinguishable photon characteristics. Wheeler's delayed-choice experiments have been extensively studied for the wave-particle duality over the last several decades to understand the complementarity theory of quantum mechanics. The heart of the delayed-choice quantum eraser is in the mutually exclusive quantum feature violating the cause-effect relation. Here, we experimentally demonstrate the quantum eraser using coherent photon pairs by the delayed choice of a polarizer placed out of the interferometer. Coherence solutions of the observed quantum eraser are derived from a typical Mach-Zehnder interferometer, where the violation of the cause-effect relation is due to selective measurements of basis choice.

Revisiting self-interference in Young's double-slit experiments.

Quantum superposition is the heart of quantum mechanics as mentioned by Dirac and Feynman. In an interferometric system, single photon self-interference has been intensively studied over the last several decades in both quantum and classical regimes. In Born rule tests, the Sorkin parameter indicates the maximum number of possible quantum superposition allowed to the input photons entering an interferometer, where multi-photon interference fringe is equivalent to that of a classical version by a laser. Here, an attenuated laser light in a quantum regime is investigated for self-interference in a Mach-Zehnder interferometer, and the results are compared with its classical version. The equivalent result supports the Born rule tests, where the classical interference originates in the superposition of individual single-photon self-interferences. This understanding sheds light on the fundamental physics of quantum features between bipartite systems.

Randomness-based macroscopic Franson-type nonlocal correlation.

Franson-type nonlocal correlation is related to Bell inequality violation tests and has been applied for quantum key distributions based on time bin methods. Using unbalanced Mach-Zehnder interferometers, Franson correlation measurements result in an interference fringe, while local measurements do not. Here, randomness-based macroscopic Franson-type correlation is presented using polarization-based two-mode coherent photons, where the quantum correlation is tested by a Hong-Ou-Mandel scheme. Coherent photons are used to investigate the wave properties of this correlation. Without contradicting the wave-particle duality of quantum mechanics, the proposed method provides fundamental understanding of the quantum nature and opens the door to deterministic quantum information science.

Observation of spin-glass-like characteristics in ferrimagnetic TbCo through energy-level-selective approach.

Rare earth (RE)-transition metal (TM) ferrimagnetic alloys are gaining increasing attention because of their potential use in the field of antiferromagnetic spintronics. The moment from RE sub-lattice primarily originates from the 4f-electrons located far below the Fermi level (EF), and the moment from TM sub-lattice arises from the 3d-electrons across the EF. Therefore, the individual magnetic moment configurations at different energy levels must be explored to clarify the microscopic mechanism of antiferromagnetic spin dynamics. Considering these issues, here we investigate the energy-level-selective magnetic moment configuration in ferrimagnetic TbCo alloy. We reveal that magnetic moments at deeper energy levels are more easily altered by the external magnetic field than those near the EF. More importantly, we find that the magnetic moments at deeper energy levels exhibit a spin-glass-like characteristics such as slow dynamics and magnetic moment freezing whereas those at EF do not. These unique energy-level-dependent characteristics of RE-TM ferrimagnet may provide a better understanding of ferrimagnet, which could be useful in spintronic applications as well as in spin-glass studies.

Experimental demonstrations of unconditional security in a purely classical regime.

So far, unconditional security in key distribution processes has been confined to quantum key distribution (QKD) protocols based on the no-cloning theorem of nonorthogonal bases. Recently, a completely different approach, the unconditionally secured classical key distribution (USCKD), has been proposed for unconditional security in the purely classical regime. Unlike QKD, both classical channels and orthogonal bases are key ingredients in USCKD, where unconditional security is provided by deterministic randomness via path superposition-based reversible unitary transformations in a coupled Mach-Zehnder interferometer. Here, the first experimental demonstration of the USCKD protocol is presented.

Analysis of phase noise effects in a coupled Mach-Zehnder interferometer for a much stabilized free-space optical link.

Recently, new physics for unconditional security in a classical key distribution (USCKD) has been proposed and demonstrated in a frame of a double Mach-Zehnder interferometer (MZI) as a proof of principle, where the unconditional security is rooted in MZI channel superposition. Due to environmental phase noise caused by temperature variations, atmospheric turbulences, and mechanical vibrations, free-space optical links have been severely challenged for both classical and quantum communications. Here, the double MZI scheme of USCKD is analyzed for greatly subdued environment-caused phase noise via double unitary transformation, resulting in potential applications of free-space optical links, where the free-space optical link has been a major research area from fundamental physics of atomic clock and quantum key distribution to potential applications of geodesy, navigation, and MIMO technologies in mobile communications systems.

Macroscopic and deterministic quantum feature generation via phase basis quantization in a cascaded interferometric system.

Quantum entanglement is the quintessence of quantum information science governed by quantum superposition mostly limited to a microscopic regime. For practical applications, however, macroscopic entanglement has an essential benefit for quantum sensing and metrology to beat its classical counterpart. Recently, a coherence approach for entanglement generation has been proposed and demonstrated in a coupled interferometric system using classical laser light, where the quantum feature of entanglement has been achieved via phase basis superposition between identical interferometric systems. Such a coherence method is based on the wave nature of a photon without violating quantum mechanics under the complementarity theory. Here, a method of phase basis quantization via phase basis superposition is presented for macroscopic entanglement in an interferometric system, which is corresponding to the energy quantization of a photon.

Macroscopically entangled light fields.

A novel method of macroscopically entangled light-pair generation is presented for a quantum laser using randomness-based deterministic phase control of coherent light in a coupled Mach-Zehnder interferometer (MZI). Unlike the particle nature-based quantum correlation in conventional quantum mechanics, the wave nature of photons is applied for collective phase control of coherent fields, resulting in a deterministically controllable nonclassical phenomenon. For the proof of principle, the entanglement between output light fields from a coupled MZI is examined using the Hong-Ou-Mandel-type anticorrelation technique, where the anticorrelation is a direct evidence of the nonclassical features in an interferometric scheme. For the generation of random phase bases between two bipartite input coherent fields, a deterministic control of opposite frequency shifts results in phase sensitive anticorrelation, which is a macroscopic quantum feature.

Coherently controlled quantum features in a coupled interferometric scheme.

Over the last several decades, entangled photon pairs generated by spontaneous parametric down conversion processes in both second-order and third-order nonlinear optical materials have been intensively studied for various quantum features such as Bell inequality violation and anticorrelation. In an interferometric scheme, anticorrelation results from photon bunching based on randomness when entangled photon pairs coincidently impinge on a beam splitter. Compared with post-measurement-based probabilistic confirmation, a coherence version has been recently proposed using the wave nature of photons. Here, the origin of quantum features in a coupled interferometric scheme is investigated using pure coherence optics. In addition, a deterministic method of entangled photon-pair generation is proposed for on-demand coherence control of quantum processing.

Control of photon storage time using phase locking.

A photon echo storage-time extension protocol is presented by using a phase locking method in a three-level backward propagation scheme, where phase locking serves as a conditional stopper of the rephasing process in conventional two-pulse photon echoes. The backward propagation scheme solves the critical problems of extremely low retrieval efficiency and pi rephasing pulse-caused spontaneous emission noise in photon echo based quantum memories. The physics of the storage time extension lies in the imminent population transfer from the excited state to an auxiliary spin state by a phase locking control pulse. We numerically demonstrate that the storage time is lengthened by spin dephasing time.

A contradictory phenomenon of deshelving pulses in a dilute medium used for lengthened photon storage time.

Lengthening of photon storage time has been an important issue in quantum memories for long distance quantum communications utilizing quantum repeaters. Atom population transfer into an auxiliary spin state has been adapted to increase photon storage time of photon echoes. In this population transfer process phase shift to the collective atoms is inevitable, where the phase recovery condition must be multiple of 2pi to satisfy rephasing mechanism. Recent adaptation of the population transfer method to atomic frequency comb (AFC) echoes [Afzelius et al., Phys. Rev. Lett. 104, 040503 (2010)], where the population transfer method is originated in a controlled reversible inhomogeneous broadening technique [Moiseev and Kroll, Phys. Rev. Lett. 87, 173601 (2001)], however, shows contradictory phenomenon violating the phase recovery condition. This contradiction in AFC is reviewed as a general case of optical locking applied to a dilute medium for an optical depth-dependent coherence leakage resulting in partial retrieval efficiency.

Tunable optical time delay of quantum signals using a prism pair.

We describe a compact, tunable, optical time-delay module that functions by means of total internal reflection within two glass prisms. The delay is controlled by small mechanical motions of the prisms. The device is inherently extremely broad band, unlike time delay modules based on "slow light" methods. In the prototype device that we fabricated, we obtain time delays as large as 1.45 ns in a device of linear dimensions of the order of 3.6 cm. We have delayed pulses with a full width at half-maximum pulse duration of 25 fs, implying a delay bandwidth product (measured in delay time divided by the FWHM pulse width) of 5.8 x 10(4). We also show that the dispersion properties of this device are sufficiently small that quantum features of a light pulse are preserved upon delay.