<p>The quantum state diffusion (QSD) equation technique has been used to effectively deal with the dynamics of the open quantum systems. Normally, the initial states of the baths are taken as vacuum states. In this paper, we use the squeezed vacuum states of the baths as the initial states. Then, the squeezing parameters are naturally introduced to the non-Markovian dynamics of the system. By using the QSD equation technique, a non-Markovian master equation in squeezed thermal baths has been derived under the weak system-bath coupling, high-temperature approximation. The dynamics of the systems can be numerically calculated by the master equation together with a group of closed <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4721_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$\overline{O}$</EquationSource> <EquationSource Format="MATHML"><math> <mover> <mi>O</mi> <mo>¯</mo> </mover> </math></EquationSource> </InlineEquation>(<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4721_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$\overline{Q}$</EquationSource> <EquationSource Format="MATHML"><math> <mover> <mi>Q</mi> <mo>¯</mo> </mover> </math></EquationSource> </InlineEquation>) operator equation. Taking a single and two-qubit coupled with the squeezed bath as examples, the dynamics of the spin state <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4721_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="35" /> </InlineMediaObject> <EquationSource Format="TEX">$\left\langle \sigma _{z}\right\rangle $</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close="〉" open="〈"> <msub> <mi>σ</mi> <mi>z</mi> </msub> </mfenced> </math></EquationSource> </InlineEquation> or correlation <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4721_Article_IEq4.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="58" /> </InlineMediaObject> <EquationSource Format="TEX">$\left\langle \sigma _{z}^{A}\sigma _{z}^{B}\right\rangle $</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close="〉" open="〈"> <msubsup> <mi>σ</mi> <mrow> <mi>z</mi> </mrow> <mi>A</mi> </msubsup> <msubsup> <mi>σ</mi> <mrow> <mi>z</mi> </mrow> <mi>B</mi> </msubsup> </mfenced> </math></EquationSource> </InlineEquation> are numerically calculated. The effects of the squeezing and memory effects on the dynamics are analyzed. For both models, big <i>p</i>-quadrature squeezing or long memory time (strong non-Markovianity) of the baths corresponds to big values of <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4721_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="35" /> </InlineMediaObject> <EquationSource Format="TEX">$\left\langle \sigma _{z}\right\rangle $</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close="〉" open="〈"> <msub> <mi>σ</mi> <mi>z</mi> </msub> </mfenced> </math></EquationSource> </InlineEquation> or <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4721_Article_IEq6.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="58" /> </InlineMediaObject> <EquationSource Format="TEX">$\left\langle \sigma _{z}^{A}\sigma _{z}^{B}\right\rangle $</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close="〉" open="〈"> <msubsup> <mi>σ</mi> <mrow> <mi>z</mi> </mrow> <mi>A</mi> </msubsup> <msubsup> <mi>σ</mi> <mrow> <mi>z</mi> </mrow> <mi>B</mi> </msubsup> </mfenced> </math></EquationSource> </InlineEquation>. When the squeezing strength is zero, the correlation functions go back to the vacuum initial state cases. The developed technique in this paper provides an effective approach to analyze the impact of multiple parameters on the systems in squeezed thermal baths.</p>

Non-Markovian dynamics of open quantum systems in squeezed thermal baths

期刊论文
发表日期：

2025年4月1日

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Arapat Ablimit,
Ahmad Abliz,
Yu-Sui Chen,
Zhao-Ming Wang

摘要

The quantum state diffusion (QSD) equation technique has been used to effectively deal with the dynamics of the open quantum systems. Normally, the initial states of the baths are taken as vacuum states. In this paper, we use the squeezed vacuum states of the baths as the initial states. Then, the squeezing parameters are naturally introduced to the non-Markovian dynamics of the system. By using the QSD equation technique, a non-Markovian master equation in squeezed thermal baths has been derived under the weak system-bath coupling, high-temperature approximation. The dynamics of the systems can be numerically calculated by the master equation together with a group of closed $\overline{O}$ $\bar{O}$ ( $\overline{Q}$ $\bar{Q}$ ) operator equation. Taking a single and two-qubit coupled with the squeezed bath as examples, the dynamics of the spin state $\left\langle \sigma _{z}\right\rangle $ $〈σ_{z}〉$ or correlation $\left\langle \sigma _{z}^{A}\sigma _{z}^{B}\right\rangle $ $〈σ_{z}^{A}, σ_{z}^{B}〉$ are numerically calculated. The effects of the squeezing and memory effects on the dynamics are analyzed. For both models, big p-quadrature squeezing or long memory time (strong non-Markovianity) of the baths corresponds to big values of $\left\langle \sigma _{z}\right\rangle $ $〈σ_{z}〉$ or $\left\langle \sigma _{z}^{A}\sigma _{z}^{B}\right\rangle $ $〈σ_{z}^{A}, σ_{z}^{B}〉$ . When the squeezing strength is zero, the correlation functions go back to the vacuum initial state cases. The developed technique in this paper provides an effective approach to analyze the impact of multiple parameters on the systems in squeezed thermal baths.