Enhancing the Performances of Autonomous Quantum Refrigerators via Two-Photon Transitions

TL;DR

The paper tackles the limitations of autonomous quantum refrigerators by enabling correlated heat transfer through two-photon transitions between hot and cold baths, introducing QRCs that outperform QRIs. It shows at least a twofold boost in cooling power and reliability, with the ratio $\langle J_c^C \rangle / \langle J_c^I \rangle > 2$, arising from increased photon flux. It further enhances performance by using synthetic negative-temperature work baths with $\beta_{sw} < 0$ realized by two work baths, enabling larger gains and a wider cooling window, including $\langle J_c^{SC} \rangle \ge \langle J_c^C \rangle$ under suitable decay-rate conditions and $\mathcal{N}_c^{SC} \le \mathcal{N}_c^C$. Thermodynamic uncertainty relation analysis shows TUR bounds of the form $\mathcal{Q}_X \ge 2$ hold across models, while QRCNs can exhibit looser bounds due to negative-temperature work baths; the approach is experimentally feasible on platforms supporting two-photon transitions.

Abstract

Conventional autonomous quantum refrigerators rely on uncorrelated heat exchange between the working system and baths via two-body interactions enabled by single-photon transitions and positive-temperature work baths, inherently limiting their cooling performance. Here, we introduce distinct qutrit refrigerators that exploit correlated heat transfer via two-photon transitions with the hot and cold baths, yielding a genuine enhancement in performance over conventional qutrit refrigerators that employ uncorrelated heat transfer. These refrigerators achieve at least a twofold enhancement in cooling power and reliability compared to conventional counterparts. Moreover, we show that cooling power and reliability can be further enhanced simultaneously by several folds, even surpassing existing cooling limits, by utilizing a synthetic negative-temperature work bath. Such refrigerators can be realized by combining correlated heat transfer and synthetic work baths, which consist of a four-level system coupled to hot and cold baths and two conventional work baths via two independent two-photon transitions. Here, the composition of two work baths effectively creates a synthetic negative-temperature work bath under suitable parameter choices. Additionally, our autonomous refrigerators with negative temperature baths significantly outperform previously studied autonomous and non-autonomous refrigerators in terms of cooling ability without requiring any additional energy resources, as they cool the cold bath to much lower temperature, which is forbidden for others refrigerators. Our results demonstrate that correlated heat transfers and baths with negative temperatures can yield thermodynamic advantages in quantum devices. Finally, we discuss the experimental feasibility of the proposed refrigerators across various existing platforms.

Figures (5)

• Figure 1: Schematic of an autonomous quantum refrigerator with correlated and uncorrelated heat transfer. The refrigerator is constituted by a three-level quantum system (qutrit), which weakly interacts with hot, cold, and work baths with the inverse temperatures $\beta_h$, $\beta_c$, and $\beta_w$, respectively. In refrigerator with uncorrelated heat transfer (QRIs), the energy transfer takes place via (independent) single photon transitions, i.e., energy levels $| 0 \rangle$ and $| 2 \rangle$ interact with the hot bath, levels $| 1 \rangle$ and $| 2 \rangle$ interact with the cold bath and levels $| 1 \rangle$ and $| 0 \rangle$ interact with the work bath, governed by the interaction Hamiltonian, given in Eq. \ref{['QRIsI']}. Solid (red, blue, and yellow) arrows indicate these independent or uncorrelated energy transfers. In refrigerator with correlated heat transfer (QRCs), the energy transfer takes place between qutrit-hot bath-cold bath via two-photon transitions, where effectively energy levels $| 0 \rangle$ and $| 1 \rangle$ participate in the process, and absorption of a photon from the hot bath is associated with the release of a photon to the cold bath and vice versa. This correlated heat transfer is governed by the interaction Hamiltonian, given in Eq. \ref{['RTT']} and indicated here by the dashed pink arrow.
• Figure 2: Plot for comparison of cooling power and noise-to-signal ratio for QRIs and QRCs. The calculations use parameters: $\omega_h = 10$, $\omega_c = 0.90$, $\omega_w = 9.10$, $\gamma_0 = 0.01$, $\beta_h = 1.00$, $\beta_w = 0.09$, and $\beta_s = 10.20$. The plot shows the ratio of cooling power (${\langle {J}^{C}_c \rangle}/{\langle {J}^{I}_c \rangle }$) (solid blue) and the ratio of noise-to-signal ratios (NSRs) in cooling power (${\mathcal{N}^{I}_c}/{\mathcal{N}^{C}_c}$) (dotted red) for QRCs and QRIs. The dashed green line marks the lower bounds for the cooling power and NSR ratios, as given by Eqs. \ref{['PFR']} and \ref{['R:NSR']}. The plot confirms that these bounds are respected. See the main text for more details.
• Figure 3: Schematic of an autonomous quantum refrigerator with correlated heat transfer and synthetic negative temperature work bath. The figure on the left side displays the refrigerator consists of a four-level quantum system weakly interacting with hot, cold, and two work baths at inverse temperatures $\beta_h$, $\beta_c$, $\beta_{w_1}$, and $\beta_{w_2}$, respectively (see main text). In these quantum refrigerators with correlated heat transfer (QRCs), energy exchange occurs via two-photon transitions involving levels $| 0 \rangle$ and $| 1 \rangle$ (indicated by the dashed pink arrow in the left figure). A photon absorbed from the hot bath is released into the cold bath, and vice versa. Simultaneously, energy transfer also takes place between the system and the two work baths through two-photon transitions, where absorption from one work bath corresponds to emission into the other (indicated by the dashed yellow arrow in the left figure). The combined effect of the two work baths can be modeled as a synthetic work bath with inverse temperature $\beta_{sw} = ({\beta_{w_1} \omega_{w_1} - \beta_{w_2} \omega_{w_2}})/({\omega_{w_1} - \omega_{w_2}})$, effectively coupled to levels $| 0 \rangle$ and $| 1 \rangle$. This refrigerator can thus be regarded as a QRCs with synthetic work baths see figure on the right side. Important to note that the temperature of synthetic work bath $\beta_{sw} = ({\beta_{w_1} \omega_{w_1} - \beta_{w_2} \omega_{w_2}})/({\omega_{w_1} - \omega_{w_2}})<0$ can be negative for the appropriate choice of system-bath parameters, if ${\beta_{w_1} \omega_{w_1} - \beta_{w_2} \omega_{w_2}}<0$. The QRCs with synthetic work bath (right side) are similar to QRCs displayed in Fig. \ref{['fig:QRCs']} except the formar utilizes the synthetic work bath, which can be negative. See main text for details.
• Figure 4: Plot for the comparison of cooling power and noise-to-signal ratio in QRCs and QRCNs. The calculations use parameters: $\omega_h= 10$, $\omega_c=0.90$, $\omega_w=9.10$, $\gamma_0 =0.01$, $\beta_h=\beta_{w_2}=1.00$, $\beta_w=\beta_{w_1} =0.09$, and $\beta_s=10.20$. (a) The figure displays $-\beta_{sw}$ against $\omega'$, to identify the region, where $\beta_{sw}$ is negative. (b) The figure in the middle shows the ratio of cooling power (${\langle {J}^{SC}_c \rangle}/{\langle {J}^{C}_c \rangle }$) corresponding to QRCs and QRNs against $\beta_c$ and $\omega'$. Note, ${\langle {J}^{SC}_c \rangle} \geq {\langle {J}^{C}_c \rangle }$ signifies that the QRCNs have more cooling power than the QRCNs, and the ratio can reach up to ${\langle {J}^{C}_c \rangle}/{\langle {J}^{I}_c \rangle } \geq 20$ for the considered scenario. (c) The figure on the right displays the ratio $\mathcal{N}^C_{c}/\mathcal{N}^{SC}_{c}$ of NSRs in cooling power corresponding to QRCs and QRNs against $\beta_c$ and $\omega'$. Note, $\mathcal{N}^{C}_{c}>\mathcal{N}_{c}^{SC}$ signifies that the QRCNs produce less NSR in power than the QRCs and the ratio can reach up to $\mathcal{N}^C_{c}/\mathcal{N}^{SC}_{c} \geq 200$ for the considered scenario. See the main text for more details.
• Figure 5: Plot for the attainability of TUR for QRIs, QRCs, and QRCNs. The calculations use parameters: $\omega_h= 10$, $\omega_c=.90$, $\omega_w=9.1$, $\gamma_0 =.01$, $\beta_h=\beta_{w_2}=1.00$, $\beta_w=\beta_{w_1} =0.09$, $\beta_s=10.20$ and $\omega'=2$. In the above figure, we plotted the $Q_{X}$ (given in Eq. \ref{['cTUR']}) against $\beta_c$, with $X\in \{I, C,SC\}$. We observed that all the refrigerator models respect the TUR (given in Eq. \ref{['cTUR']}). See the main text for more details.