[Paper Review] Macroscopic entanglement between wave-packets at nite temperature

Ana María Guerra Martins|arXiv (Cornell University)|Jan 1, 2014

Spectroscopy and Quantum Chemical Studies1 references3 citations

TL;DR

This paper investigates macroscopic entanglement between wave-packets at finite temperature using collective operators derived from Fourier-transformed microscopic mode amplitudes, modeling two MPDC interaction patterns—pairwise and one-to-all. It finds that macroscopic entanglement grows linearly with mode count in the one-to-all pattern, while remaining constant in the pairwise case, with lower critical temperatures and earlier entanglement birth times as mode count increases.

ABSTRACT

We investigate entanglement between collective operators of two wavepackets of nite spectral bandwidth, in two dierent approximations of the Multimode Parametric-Down Conversion (MPDC) process: the pairwise and the one-to-all interaction patterns. For collective operators we choose the macroscopic amplitudes of each wave-packet dened by the Fourier Transform of their microscopic mode amplitudes. This approach intends, to respond to realistic experimental conditions, where measurements apparatuses may not resolve single microscopic mode amplitudes but rather the collective amplitude of the wave-packets. To quantify the bipartite macroscopic entanglement we use the logarithmic negativity. We relate the time dependent degree of macroscopic entanglement with the complexity (number of modes and interaction pattern) and the temperature of the system. Our results show that the macroscopic entanglement increases linearly with the number of micro-modes in the case of the one-to-all interaction, while in the pairwise interaction it is constant. Moreover, in the one-to-all pattern the birth time of entanglement and the critical temperature decrease with increasing the number of micro-modes. We draw the graphs associated with the two interaction patterns and related the degree of collective entanglement with the connectivity and the index of each vertex (mode) of the graph. We conclude that quantum information and computation tasks may be achieved more eciently by manipulating appropriated collective operators in some macroscopic systems, then by using their microscopic counterparts.

Motivation & Objective

• To model realistic experimental conditions where detectors resolve collective wave-packet amplitudes rather than individual microscopic modes.
• To quantify bipartite macroscopic entanglement using logarithmic negativity as a measure under finite-temperature conditions.
• To compare the impact of two distinct multimode parametric down-conversion interaction patterns—pairwise and one-to-all—on entanglement dynamics.
• To analyze how the number of micro-modes and system temperature influence the onset and degree of macroscopic entanglement.
• To explore the potential of collective operators for more efficient quantum information tasks in macroscopic systems.

Proposed method

• Define macroscopic amplitudes of wave-packets via the Fourier transform of microscopic mode amplitudes to reflect measurable collective observables.
• Model the Multimode Parametric-Down Conversion (MPDC) process using two interaction patterns: pairwise (one-to-one mode coupling) and one-to-all (all modes coupled to a central mode).
• Use logarithmic negativity as the entanglement measure to quantify bipartite macroscopic entanglement between the two wave-packets.
• Analyze time-dependent entanglement dynamics while varying the number of micro-modes and system temperature.
• Represent the interaction patterns as graphs, relating entanglement to vertex connectivity and mode index (degree of each mode).
• Derive and compare the evolution of entanglement for both interaction patterns under finite-temperature conditions.

Experimental results

Research questions

• RQ1 How does the number of micro-modes affect the degree of macroscopic entanglement in the one-to-all MPDC interaction pattern?
• RQ2 How does the pairwise interaction pattern compare to the one-to-all pattern in terms of entanglement generation and stability?
• RQ3 What is the relationship between the number of micro-modes and the critical temperature for entanglement in each interaction model?
• RQ4 How does the birth time of entanglement depend on the number of micro-modes in the one-to-all configuration?
• RQ5 Can collective operators in macroscopic systems outperform microscopic modes in enabling quantum information tasks?

Key findings

• In the one-to-all interaction pattern, macroscopic entanglement increases linearly with the number of micro-modes.
• In the pairwise interaction pattern, macroscopic entanglement remains constant regardless of the number of micro-modes.
• The birth time of entanglement decreases with increasing micro-mode count in the one-to-all pattern, indicating earlier entanglement onset.
• The critical temperature for entanglement decreases with increasing micro-mode count in the one-to-all pattern.
• Entanglement dynamics correlate with graph-theoretic properties: vertex connectivity and mode index influence the degree of collective entanglement.
• Manipulating collective operators in macroscopic systems offers a more efficient pathway for quantum information and computation tasks than using microscopic modes.